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BEGIN:VEVENT
SUMMARY:Christoph Kawan (LMU München\, Germany)
DTSTART;VALUE=DATE-TIME:20210708T150000Z
DTEND;VALUE=DATE-TIME:20210708T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/1
DESCRIPTION:Title: A Lyapunov-based small-gain approach to ISS of infinite nonlinear netwo
rks\nby Christoph Kawan (LMU München\, Germany) as part of Input-to-S
tate Stability and its Applications\n\n\nAbstract\nIn this talk\, I presen
t an approach to the verification of\ninput-to-state stability for network
ed control systems composed of a\ncountably infinite number of nonlinear s
ubsystems. The essential\nrequirements on these subsystems are that they a
re finite-dimensional\,\ncontinuous in time and each of them is influenced
only by finitely many\nother subsystems. Assuming that each subsystem adm
its an ISS Lyapunov\nfunction with respect to both internal inputs (influe
nces from other\nsubsystems) and external inputs (control inputs)\, our re
sult provides\nsufficient conditions for the existence of an ISS Lyapunov
function for\nthe whole network. This Lyapunov function is built from the
Lyapunov\nfunctions of the subsystems and it is important to note that the
ISS\nestimates for the later are given in the max-type formulation. This\
nformulation allows for the definition of an associated max-type gain\nope
rator Gamma\, encoding the influence of the\nsubsystems on each other via
nonlinear gain functions. The operator\nGamma acts as a monotone operator
on the positive cone of \\ell_{\\infty}.\nThe essential requirement on Gam
ma is that it admits a so-called path of\nstrict decay\, a condition which
is known to be equivalent to the\nclassical small-gain condition in the c
ase of finite networks. For\ninfinite networks\, however\, this equivalenc
e does not hold. Still\, as in\nfinite dimensions\, the existence of a pat
h of strict decay is linked to\nthe stability properties of the discrete-t
ime system generated by the\ngain operator. In my talk\, I will try to\nex
plain the difficulties involved with the stability analysis of this\nsyste
m.\n\nJoint work with Andrii Mironchenko and Majid Zamani\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iasson Karafyllis (National Technical University of Athens\, Greec
e)
DTSTART;VALUE=DATE-TIME:20210715T150000Z
DTEND;VALUE=DATE-TIME:20210715T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/2
DESCRIPTION:Title: IOS-gains and asymptotic gains for linear systems\nby Iasson Karafy
llis (National Technical University of Athens\, Greece) as part of Input-t
o-State Stability and its Applications\n\n\nAbstract\nThe talk will be dev
oted to the presentation of a fundamental relation between Output \nAsympt
otic Gains (OAG) and Input-to-Output Stability (IOS) gains for li
near \nsystems. More specifically\, it will be shown that for eve
ry Input-to-State Stable\, \nstrictly causal linear system the minimum O
AG is equal to the minimum IOS-gain. \nMoreover\, both quantities can
be computed by solving a specific optimal control \nproblem and by
considering periodic inputs only. The result is valid for wide classes \no
f linear systems (including delay systems or systems described by
PDEs). The \ncharacterization of the minimum IOS-gain is importan
t because it allows the non-\nconservative computation of the IOS
-gains\, which can be used in a small-gain \nanalysis. A number
of cases of finite-dimensional linear systems will also be \nprese
nted\, where exact computation of the minimum IOS-gain can be pe
rformed. \nLinks to notions used extensively in the literature of linear s
ystems (e.g.\, the BIBO \nnorm or the notion of an admissible operator) wi
ll be provided.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miroslav Krstic (UC San Diego\, USA)
DTSTART;VALUE=DATE-TIME:20210722T150000Z
DTEND;VALUE=DATE-TIME:20210722T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/3
DESCRIPTION:Title: Fixed-Time ISS and Prescribed-Time Stabilization\nby Miroslav Krsti
c (UC San Diego\, USA) as part of Input-to-State Stability and its Applica
tions\n\n\nAbstract\nIn prescribed-time stabilization the task is to desig
n a feedback law that guarantees completion of the convergence to a set po
int no later than a time that is prescribed by the user and independent of
the initial condition of the plant. When the plant model is known perfect
ly and the full state is measured\, ISS issues do not arise. However\, in
the presence of disturbances or under observer-based feedback\, ISS with r
espect to various inputs becomes of interest. Perhaps unexpectedly\, once
prescribed-time stabilization is achieved\, an ISS-like property stronger
than the conventional ISS is obtained as a bonus. Specifically\, the origi
n\, which is not necessarily the system’s equilibrium\, is made attracti
ve in prescribed time even in the presence of non-vanishing disturbances.
Or\, in simpler language\, the ISS gain is a function of time and decays t
o zero at the terminal time. I will discuss the ISS issues associated with
prescribed-time feedback design for general linear ODEs\, some nonlinear
ODEs with a disturbance matched by control\, and briefly for parabolic PDE
s (in hyperbolic PDEs\, finite-time stabilization\, when possible\, is obt
ained as easily as exponential stabilization).\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Postoyan (CNRS\, Université de Lorraine\, France)
DTSTART;VALUE=DATE-TIME:20210729T150000Z
DTEND;VALUE=DATE-TIME:20210729T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/4
DESCRIPTION:Title: Event-Triggered Control Through the Eyes of Hybrid Small-Gain Theorem\nby Romain Postoyan (CNRS\, Université de Lorraine\, France) as part o
f Input-to-State Stability and its Applications\n\n\nAbstract\nA common ap
proach to design event-triggered controllers is emulation. The idea is to
first construct a feedback law in continuous-time\, which ensures the desi
red closed-loop properties. Then\, the communication constraints between t
he plant and the controller are taken into account and a triggering rule i
s synthesized to generate the transmission instants in such a way that the
properties of the continuous-time closed-loop system are preserved\, and
a strictly positive minimum inter-event time exists\, which is essential i
n practice.\n\nVarious triggering rules have been proposed in this context
in the literature\, including relative threshold\, fixed threshold\, dyna
mic triggering law to mention a few. We will show in this talk that these
seemingly unrelated techniques can all be interpreted in a unified manner.
Indeed\, it appears that all them guarantee the satisfaction of the condi
tions of a hybrid small-gain theorem. This unifying perspective provides c
lear viewpoints on the essential differences and similarities of existing
event-triggering policies. Interestingly\, for all the considered laws\, t
he small-gain condition vacuously holds in the sense that one of the inter
connection gains is zero. We then exploit this fact to modify the original
triggering law in such a way that the small-gain condition is no longer t
rivially satisfied. By doing so\, we obtain redesigned strategies\, which
may reduce the number of transmissions as illustrated by an example.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Polyakov (Inria Lille Nord-Europe / CNRS CRIStAL)
DTSTART;VALUE=DATE-TIME:20211007T150000Z
DTEND;VALUE=DATE-TIME:20211007T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/6
DESCRIPTION:Title: On Input-to-State Stability of Homogeneous Evolution Equations\nby
Andrey Polyakov (Inria Lille Nord-Europe / CNRS CRIStAL) as part of Input-
to-State Stability and its Applications\n\n\nAbstract\nHomogeneity is a sy
mmetry of an object with respect to a dilatation. All linear and many\nnon
linear models of mathematical physics are homogeneous. For example\, Burge
rs\, KdV and Navier-Stokes \nequations are symmetric with respect to a pro
perly selected dilation. Finite dimensional homogeneous control\nsystems
are known to be similar with linear ones\, but they may have a better reg
ulation quality like\na faster convergence\, stronger robustness and less
overshoot. This talk is devoted to Input-to-State Stability analysis\nof
homogeneous evolution equations in Banach spaces. Similarly to the finite-
time dimensional case\, it is shown that\nthe uniform asymptotic stability
of homogeneous unperturbed system guarantees its Input-to-State Stability
\nwith respect to homogeneously involved perturbations.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Chaillet (L2S - CentraleSupélec - Univ. Paris Saclay)
DTSTART;VALUE=DATE-TIME:20211028T150000Z
DTEND;VALUE=DATE-TIME:20211028T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/7
DESCRIPTION:Title: Point-wise dissipation in time-delay systems: recent results and open q
uestions\nby Antoine Chaillet (L2S - CentraleSupélec - Univ. Paris Sa
clay) as part of Input-to-State Stability and its Applications\n\n\nAbstra
ct\nIn the existing characterizations of input-to-state stability (ISS) fo
r time-delay systems\, the Lyapunov-Krasovskii functional (LKF) has a $\\m
athcal K_\\infty$ dissipation rate that involves the whole LKF itself (LKF
-wise dissipation) or even the supremum norm of the state history (history
-wise dissipation). A similar characterization holds for integral input-to
-state stability (iISS)\, in which the dissipation rate is just a positive
definite function. These characterizations have allowed to extend several
results on ISS and iISS from finite dimension to time-delay systems.\n\nN
evertheless\, in practice\, obtaining a LKF-wise or history-wise dissipati
on is not always an easy task and often resorts to rather artificial trick
s. More crucially\, in the absence of inputs\, it is known from the work o
f N. Krasovskii that a dissipation involving merely the current value of t
he state norm (point-wise dissipation) is enough to guarantee global asymp
totic stability.\n\nIn this talk\, we investigate whether a point-wise dis
sipation suffices to conclude ISS or iISS for time-delay systems. We give
a positive answer to this question for iISS. More precisely\, we show that
point-wise\, LKF-wise and history-wise dissipations through a positive de
finite function all ensure iISS. \n\nFor ISS\, despite strong efforts\, th
is question remains open: it has not yet be proved or disproved that ISS i
s equivalent to the existence of a point-wise dissipation. We identify two
classes of systems for which this is the case\, by imposing a growth rest
riction either on the upper bound of the LKF or on the vector field. We al
so provide some insights on what can be said about a system having a point
-wise dissipation to hopefully foster some creative discussion.\n\nFinally
\, while asymptotic stability is known for long to be equivalent to a poin
t-wise dissipation for input-free systems\, this question remains open for
exponential stability. We show that\, at least for systems ruled by a glo
bally Lipschitz vector field\, global exponential stability is guaranteed
under a point-wise dissipation.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No Seminar this week\, but consider taking part in the SCINDIS Wo
rkshop (27-29 Sep 2021\, fully online\, zero conference fee)
DTSTART;VALUE=DATE-TIME:20210930T150000Z
DTEND;VALUE=DATE-TIME:20210930T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/8
DESCRIPTION:Title: 3rd Workshop on Stability and Control of Infinite-Dimensional Systems (
SCINDIS 2020)\nby No Seminar this week\, but consider taking part in t
he SCINDIS Workshop (27-29 Sep 2021\, fully online\, zero conference fee)
as part of Input-to-State Stability and its Applications\n\n\nAbstract\nV
isit the homepage of SCINDIS:\nhttps://www.fan.uni-wuppertal.de/de/scindis
-2020.html\n\nThe scope of the Workshop includes but is not limited to\n
\n >Stability and control of partial differential equations\n >Stability
and control of time-delay systems\n >Input-to-state stability of infinit
e-dimensional systems\n >Stabilizability of infinite-dimensional systems\
n >Semigroup and admissibility theory\n\nOrganizers:\nSergey Dashkovskiy\
nBirgit Jacob \nAndrii Mironchenko\nFabian Wirth\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rami Katz (Tel-Aviv University\, Israel)
DTSTART;VALUE=DATE-TIME:20211209T160000Z
DTEND;VALUE=DATE-TIME:20211209T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/10
DESCRIPTION:Title: Finite-dimensional observer-based ISS and $L^2$-gain control of parabo
lic PDEs\nby Rami Katz (Tel-Aviv University\, Israel) as part of Input
-to-State Stability and its Applications\n\n\nAbstract\nFinite-dimensional
observer-based controller design for PDEs is a challenging problem. In th
is talk\, construction of such controllers via the modal decomposition met
hod for linear parabolic 1D PDEs will be presented. We will start with fin
ite-dimensional observer-based control for the linear heat equation where
at least one of the control or observation operators is bounded. We will p
roceed with the case of both operators unbounded\, where dynamic extension
is helpful. Here we will consider ISS and $L^2$-gain analysis of the Kura
moto-Sivashinsky equation. The extension of the results to time-varying in
put/output delays\, as well as arbitrarily large constant input delays wil
l be presented. Finally\, we will discuss sampled-data implementation of
ﬁnite-dimensional boundary controllers for the 1D heat equation under di
screte-time point measurement\, via a generalized hold device. An essentia
l tool for the ISS analysis will be a novel ISS Halanay’s inequality wit
h explicit constants in the bounds.\n\nJoint work with Prof. Emilia Fridma
n\nhttps://scholar.google.co.il/citations?user=szPJQlkAAAAJ&hl=en\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Schwenninger (TU Twente\, the Netherlands)
DTSTART;VALUE=DATE-TIME:20211202T160000Z
DTEND;VALUE=DATE-TIME:20211202T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/11
DESCRIPTION:Title: Recent results on ISS Lyapunov functions\nby Felix Schwenninger (T
U Twente\, the Netherlands) as part of Input-to-State Stability and its Ap
plications\n\n\nAbstract\nLike in many branches of dynamical systems\, Lya
punov functions play a pivotal role in the study of input-to-state stabili
ty.\nIn this talk we discuss recent investigations around such coercive an
d non-coercive Lyapunov functions in the context of infinite-dimensional s
ystems. A focus is laid on general linear PDEs subject to boundary control
.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ricardo Sanfelice (University of California\, Santa Cruz\, USA)
DTSTART;VALUE=DATE-TIME:20211118T160000Z
DTEND;VALUE=DATE-TIME:20211118T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/12
DESCRIPTION:Title: Observers for Hybrid Dynamical Systems: Models\, Necessary Conditions\
, and Systematic Design\nby Ricardo Sanfelice (University of Californi
a\, Santa Cruz\, USA) as part of Input-to-State Stability and its Applicat
ions\n\n\nAbstract\nIn most control applications\, estimating the state of
a system is crucial\, whether it be for control\, supervision\, or fault
diagnosis purposes. Unfortunately\, the problem of designing observers for
systems with state variables that evolve continuously\, and at times\, ju
mp -- namely\, hybrid systems -- in a general setting is unsolved. One of
the main challenges in the design of observers for such systems is the fa
ct that hybrid behavior may lead to system trajectories from nearby initia
l conditions that have different jump times. Such a mismatch of jump times
makes the formulation of observability/detectability and\, in turn\, obse
rver design very challenging. After a brief introduction to hybrid dynami
cal systems\, recent advancements towards the systematic design of observe
rs for hybrid systems will be presented. Specifically\, a general framew
ork for state estimation of plants modeled as hybrid dynamical systems\, b
oth in the favorable case where the jumps of the plant and of the observer
occur at the same time and when they occur at different (but nearby) time
s\, will be introduced. With a suitable notion of observer for hybrid dyn
amical systems and relying on reparameterizations of the hybrid signals in
volved\, it will be shown that an appropriate detectability notion is nece
ssary for the existence of an observer\, or better said\, a hybrid observe
r. Applications and examples will be presented to illustrate the concepts
and results. This research is joint work with Professor Pauline Bernard
at MINES ParisTech (https://sites.google.com/site/sitepmbernard/home).\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aneel Tanwani (LAAS-CNRS\, Toulouse\, France)
DTSTART;VALUE=DATE-TIME:20220113T160000Z
DTEND;VALUE=DATE-TIME:20220113T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/13
DESCRIPTION:Title: Input-to-State Stability of Switched Systems under Dwell-Time Conditio
ns\nby Aneel Tanwani (LAAS-CNRS\, Toulouse\, France) as part of Input-
to-State Stability and its Applications\n\n\nAbstract\nAbstract: Stability
analysis of switched systems has been a topic of interest for more than t
wo decades\, and the conditions based on dwell-time notions form an import
ant part of this literature. In particular\, input-to-state stability (ISS
) and different variants of ISS have also been studied using similar dwell
-time conditions on the switching signals. Earlier approaches in this dire
ction\, based on multiple Lyapunov functions\, typically require exponenti
ally decaying Lyapunov functions which are compatible with other subsystem
s. However\, such compatibility may not hold for switched nonlinear system
s in general\, where the individual Lyapunov functions admit nonlinear sup
ply functions. In this talk\, I will start with a quick overview of earlie
r results on ISS using dwell-time conditions. Then\, I will provide some e
xamples of switched nonlinear systems which are not ISS for arbitrarily la
rge values of dwell-time\, even though individual subsystems are ISS. Neve
rtheless\, under certain conditions on Lyapunov functions (which admit non
linear supply functions)\, we can derive new dwell-time bounds\, which gua
rantee ISS of switched systems. We will see the utility of such conditions
in analyzing stability of cascade interconnections of switched systems an
d an application in sampled-data control using dynamic output feedback.\n\
nReferences:\n[1] M. Della Rossa and A. Tanwani. Instability of Dwell-Time
Constrained Switched Nonlinear Systems. Under review in Systems & Control
Letters\, June 2021. Preprint available on request.\n[2] S. Liu\, A. Tanw
ani and D. Liberzon. ISS and Integral ISS of Switched Systems with Nonline
ar Supply Functions. Mathematics of Controls\, Signals\, and Systems\, 202
1. DOI: 10.1007/s00498-021-00306-x\n[3] G.X. Zhang and A. Tanwani. ISS Lya
punov Functions for Cascade Switched Systems and Sampled-Data Control\, Au
tomatica\, 105: 216—227\, 2019.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierdomenico Pepe (University of L'Aquila)
DTSTART;VALUE=DATE-TIME:20220120T160000Z
DTEND;VALUE=DATE-TIME:20220120T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/14
DESCRIPTION:Title: Nonlinear Halanay's Inequalities for ISS of Retarded Systems: the Cont
inuous and the Discrete Time Case\nby Pierdomenico Pepe (University of
L'Aquila) as part of Input-to-State Stability and its Applications\n\n\nA
bstract\nNonlinear versions of continuous-time and discrete-time Halanay's
inequalities are presented as sufficient conditions for the convergence o
f involved functions to the origin\, uniformly with respect to bounded set
s of initial values. The same results are shown in the case forcing terms
are also present\, for the uniform convergence to suitable neighborhoods o
f the origin. Related Lyapunov methods for the global uniform asymptotic s
tability and the input-to-state stability of systems described by retarded
functional differential equations and by discrete-time equations with del
ays are shown. \n\nReferences:\n[1] Pierdomenico Pepe\, A Nonlinear Versio
n of Halanay’s Inequality for the Uniform Convergence to the Origin\, Ma
thematical Control and Related Fields\, 2021\, doi: 10.3934/mcrf.2021045
\n\n[2] Maria Teresa Grifa\, Pierdomenico Pepe\, On Stability Analysis of
Discrete-Time Systems With Constrained Time-Delays via Nonlinear Halanay-T
ype Inequality\, IEEE Control Systems Letters\, Volume 5\, Issue 3\, July
2021\, doi: 10.1109/LCSYS.2020.3007096\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wilfrid Perruquetti (Ecole Centrale de Lille\, CNRS\, France)
DTSTART;VALUE=DATE-TIME:20220203T160000Z
DTEND;VALUE=DATE-TIME:20220203T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/15
DESCRIPTION:Title: Non-Asymptotic output feedback of a double integrator: a separation pr
inciple.\nby Wilfrid Perruquetti (Ecole Centrale de Lille\, CNRS\, Fra
nce) as part of Input-to-State Stability and its Applications\n\n\nAbstrac
t\nUsually\, in control/estimation problems\, one is looking at exponentia
l decaying rates for many reasons: ease of understanding\, many tools for
tuning and getting a time response estimate. But nowadays\, control theory
has to meet more and more demanding performances in many areas such as ae
rospace\, manufacturing\, robotics and transportation to mention a few. A
necessary property for these algorithms is stability. The convergence time
for the system to reach the goal may be infinite (e.g.\, asymptotic or ex
ponential convergence) or finite. Combining stability with these convergen
ce types leads to asymptotic or non-asymptotic stability properties. \n\nT
hese concepts may help in obtaining a separation principle when designing
output feedback as seen on an example for an double integrator system wher
e ISS properties of homogeneous systems is applied without building a Lyap
unov function for the closed-loop system.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Guiver (Edinburgh Napier University)
DTSTART;VALUE=DATE-TIME:20220210T160000Z
DTEND;VALUE=DATE-TIME:20220210T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/16
DESCRIPTION:Title: The exponential input-to-state stability property — characterisation
s and feedback interconnections\nby Chris Guiver (Edinburgh Napier Uni
versity) as part of Input-to-State Stability and its Applications\n\n\nAbs
tract\nThe exponential input-to-state stability (ISS) property is consider
ed for systems of controlled nonlinear differential equations\, and a char
acterisation in terms of an exponential ISS Lyapunov function is establish
ed. A natural concept of linear state/input-to-state L2-gain is\nintroduce
d\, and the equivalence of this property and exponential ISS is establishe
d. Further\, the feedback interconnection of two exponentially ISS systems
is shown to be exponentially ISS provided a suitable small-gain condition
is satisfied.\n\nJoint work with Hartmut Logemann\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lars Grüne (University of Bayreuth)
DTSTART;VALUE=DATE-TIME:20230531T150000Z
DTEND;VALUE=DATE-TIME:20230531T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/17
DESCRIPTION:Title: Curse-of-dimensionality-free computation of (control-)Lyapunov functio
ns via ISS small-gain techniques and neural networks\nby Lars Grüne (
University of Bayreuth) as part of Input-to-State Stability and its Applic
ations\n\n\nAbstract\nThe literature reports a large number of computation
al methods for Lyapunov and control Lyapunov functions. For most of these
approaches the computational effort grows exponentially in the state space
dimension\, making them infeasible even for moderately high-dimensional p
roblems. In this talk we show that this so-called curse of dimensionality
can be overcome for Lyapunov functions with a suitable separable structure
\, as they are provided by ISS small-gain theory.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Wirth (University of Passau\, Germany)
DTSTART;VALUE=DATE-TIME:20230614T150000Z
DTEND;VALUE=DATE-TIME:20230614T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/18
DESCRIPTION:Title: Variants of Two-Measure Input-to-State Stability\nby Fabian Wirth
(University of Passau\, Germany) as part of Input-to-State Stability and i
ts Applications\n\n\nAbstract\nThis talk is based on joint work with Chris
topher Kellett\n\nThis talk concerns finite-dimensional systems described
by ordinary differential equations with inputs.\nFor attracting closed set
s that are not compact we consider different formulations of input-to-stat
e stability properties and related Lyapunov criteria. In the compact case
\, there exists a well-established hierarchy of such properties and some f
ormulations have been quickly discarded as equivalent to input-to-state st
ability. In the noncompact case\, however\, several new phenomena appear.
In particular\, input-to-state stability (ISS) does not imply integral in
put-to-state stability\, and ISS is not equivalent to integral-input-to-in
tegral-state stability. The criteria are formulated in terms of measuremen
t functions\, which allows a uniform presentation of a number of related r
esults. Some examples are discussed to show some of the phenomena that may
occur.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christophe Prieur (CNRS\, University Grenoble Alpes\, France)
DTSTART;VALUE=DATE-TIME:20230621T150000Z
DTEND;VALUE=DATE-TIME:20230621T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/19
DESCRIPTION:Title: Boundary feedback stabilization of freeway traffic networks: ISS contr
ol and experiments\nby Christophe Prieur (CNRS\, University Grenoble A
lpes\, France) as part of Input-to-State Stability and its Applications\n\
n\nAbstract\nBoundary feedback control of networks of freeway traffic is c
onsidered in this talk by means of\nPartial Differential Equations based t
echniques and Lyapunov theory. The control and measurements are all locate
d at the boundaries of each link. In this talk we will study some publishe
d and on-going works on the control of these dynamics and on the design pr
oblem of boundary controls ensuring an Input-to-State Stability property i
n presence of disturbances. Finally some results will be illustrated using
a traffic simulation software at the Fourth Ring road of Beijing\, China
when some specific traffic data are collected and the sufficient condition
s for the stability are checked.\n\n**Biography:** Christophe PRIEUR gr
aduated in Mathematics from the Ecole Normale Supérieure de Cachan\, Fran
ce in 2000. He received the Ph.D degree in 2001 in Applied Mathematics fro
m the Université Paris-Sud\, France. From 2002 he was an associate resear
cher CNRS at the laboratory SATIE\, Cachan\, France\, and at the LAAS\, To
ulouse\, France (2004-2010). In 2010 he joined the Gipsa-lab\, Grenoble\,
France where he is currently a senior researcher of the CNRS (since 2011).
He was the Program Chair of the 9th IFAC Symposium on Nonlinear Control S
ystems (NOLCOS 2013)\, the 14th European Control Conference (ECC 2015) and
the 61st IEEE Conference on Decision and Control (CDC 2022). He is curren
tly an associate editor of the AIMS Evolution Equations and Control Theory
\, the SIAM Journal of Control and Optimization and the Mathematics of Con
trol\, Signals\, and Systems. He is a senior editor of the IEEE Control Sy
stems Letters\, and an editor of the IMA Journal of Mathematical Control a
nd Information. His current research interests include nonlinear control t
heory\, hybrid systems\, and control of partial differential equations\, w
ith applications including navigation and object tracking\, fluid dynamics
\, and fusion control. He is an IMA Fellow\, and an IEEE Fellow.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Luis Mancilla-Aguilar (Universidad de Buenos Aires\, Argenti
na)
DTSTART;VALUE=DATE-TIME:20230607T150000Z
DTEND;VALUE=DATE-TIME:20230607T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/20
DESCRIPTION:Title: From ISS to iISS without the use of Lyapunov functions: a difficult pa
th leading to greater generality\nby José Luis Mancilla-Aguilar (Univ
ersidad de Buenos Aires\, Argentina) as part of Input-to-State Stability a
nd its Applications\n\n\nAbstract\nIt is well-known that input-to-state (I
SS) stability implies integral ISS (iISS) for time-invariant finite dimens
ional systems. The original proof of this fact is heavily based on the exi
stence of an ISS dissipation-form Lyapunov function. When one tries to pro
ve the implication for time-varying systems two obstacles appear: a) there
are ISS systems that are not iISS and b) existing converse theorems provi
de ISS implication-form Lyapunov functions that may not be necessarily dis
sipation-form ones. In this presentation we talk about the way we found f
or proving that ISS implies iISS avoiding the use of Lyapunov functions an
d how this allows us to prove that implication for other types of time-var
ying systems\, such as impulsive and switched systems. We also present a c
haracterization of iISS\, which holds even for axiomatically defined syste
ms\, that was crucial in our approach for proving that ISS is stronger tha
n iISS under suitable hypotheses. \n\nIt is joint work with Hernan Haimovi
ch and Jose Esteban Rojas-Ruiz.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marius Tucsnak (Université de Bordeaux\, France)
DTSTART;VALUE=DATE-TIME:20230628T150000Z
DTEND;VALUE=DATE-TIME:20230628T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/21
DESCRIPTION:Title: ISS type properties of some fluid dynamics systems\nby Marius Tucs
nak (Université de Bordeaux\, France) as part of Input-to-State Stability
and its Applications\n\n\nAbstract\nWe consider systems describing viscou
s fluid flows\, possibly in interaction with rigid bodies\, moving at the
interior or floating on the free surface of the fluid. We briefly present
the case when the fluid is contained in a bounded container. Exploiting th
e exponential stability of the linearized system we show that in this case
we can obtain ISS type estimates for fully nonlinear problems. The focus
is on the case when the fluid fills the whole space (with the possible exc
eption of a bounded moving rigid body). In this case the linearized system
is not exponentially and not even polynomially stable. In this case we
prove a nonstandard type of ISS estimates for the linearized systems. We f
inally explain how to obtain wellposedness results for fully nonlinear fl
uid-structure interaction in unbounded domains and formulate some conjectu
res on the ISS properties of these systems.\n\n**Biography:** Marius Tu
csnak is Professor of Mathematics of the University of Bordeaux in France.
He holds a Master degree in mathematics from the University of Bucarest\,
Romania and a Ph.D. degree from the University of Orléans\, France (1992
). In 1995 he obtained his Habilitation pour Diriger les Recherches from t
he “Université Pierre et Marie Curie”\, Paris. In 1992 he became Asso
ciate Professor of Mathematics at the University of Versailles\, France. I
n 1997 he became full professor of mathematics at the University of Nancy\
, France. He moved to University of Bordeaux in 2015. \nHe was an invited
speaker to the International Congress of Mathematicians (ICM)\, 2022\, and
since 2013 he is a Member of Institut Universitaire de France (IUF). \nHi
s fields of expertise are the analysis and the control of systems governed
by partial differential equations. One of his major recent contributions
is his participation at a series of works which solved a long standing ope
n problem: the full characterization of the reachable space for the bounda
ry controlled one dimensional heat equation.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swann Marx (CNRS\, Nantes\, France)
DTSTART;VALUE=DATE-TIME:20230524T150000Z
DTEND;VALUE=DATE-TIME:20230524T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/22
DESCRIPTION:Title: ISS Lyapunov functional strictification for the output regulation of a
Korteweg-de Vries equation\nby Swann Marx (CNRS\, Nantes\, France) as
part of Input-to-State Stability and its Applications\n\n\nAbstract\nThis
talk will be about the construction of a strict ISS Lyapunov functional i
n order to design a controller achieving an output regulation task for a K
orteweg-de Vries equation. To be more precise\, our goal is to add an inte
grator so that one is able to make converging a given output to a desired
reference. To do so\, a forwarding method will be used together with the c
onstruction of a ISS strict Lyapunov functional\, that is necessary to app
ly the above mentioned method. The strictification technique is based on a
recent method\, developed in the finite-dimensional context by Laurent Pr
aly\, and that relies on the construction of an observer. In our context\,
this observer is built thanks to the backstepping method. It is joint wor
k with Ismaïla Balogoun and Daniele Astolfi.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Dashkovskiy (University of Würzburg\, Germany)
DTSTART;VALUE=DATE-TIME:20230705T150000Z
DTEND;VALUE=DATE-TIME:20230705T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/23
DESCRIPTION:Title: Interconnected systems with possibly unstable subsystems\nby Serge
y Dashkovskiy (University of Würzburg\, Germany) as part of Input-to-Stat
e Stability and its Applications\n\n\nAbstract\nSmall-gain theory is known
to be very useful in studying stability of\ninterconnected systems. This
theory is well-developed for very large\nclasses of essentially nonlinear
systems. This theory presumes that each\nsubsystem of an interconnection s
atisfies certain stability properties.\nHowever\, if some subsystems are n
ot stable\, then small-gain conditions\ncannot be applied and we cannot co
nclude about stability of the whole\nsystem. Only a few extensions of the
small-gain theory exist\, where\nsubsystems allowed to be not stable. More
general approaches should be\ndeveloped. In this presentation we demonstr
ate a new approach in this\ndirection\, which is based on positivity prope
rties with respect to a\nspecial cone. With this approach we derive suffic
ient stability\nconditions for a feedback connection of two subsystems\, w
here one of\nthem can be not stable. In case both subsystems are stable\,
the\nsmall-gain approach can be applied as well. Hence a comparison with\n
small-gain condition is possible and is provided here. So far our\nresults
are also restricted to a rather narrow class of systems\, however\nextens
ions and developments to more general systems seem to be\nrealistic\, whic
h we discuss briefly at the end.\n\n**Biography:**\nSergey Dashkovskiy
received the M.Sc. degree in applied mathematics in\n1996 from the Lomonos
sov University of Moscow and Ph.D. degree in\nMathematics in 2002 from the
University of Jena. He has got his\nhabilitation (venia legendi) in Mathe
matics in 2009 from the university\nBremen.\nHe held positions at the Ariz
ona State University\, the University of\nBayreuth and the University of A
pplied Scienses Erfurt.\nSince 2016 he is professor and head of the resear
ch group Dynamics and\nControl at the Institute for Mathematics\, Universi
ty of Würzburg.\nHis research interests are in stability theory of dynami
cal systems and\nnetworks.\nHe is editorial board member of several journa
ls related to this\nresearch area\, in particular\, of IEEE Transactions o
n Automatic Control\nand Nonlinear Analysis: Hybrid Systems.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masashi Wakaiki (Kobe University\, Japan)
DTSTART;VALUE=DATE-TIME:20230809T150000Z
DTEND;VALUE=DATE-TIME:20230809T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/24
DESCRIPTION:Title: Semi-uniform ISS and iISS of infinite-dimensional systems\nby Masa
shi Wakaiki (Kobe University\, Japan) as part of Input-to-State Stability
and its Applications\n\n\nAbstract\nIf an infinite-dimensional system is s
trongly stable but not exponentially stable\, a rate of decay is not expec
ted to be uniform for all solutions. Nevertheless\, one may establish a un
iform estimate on decay rates for all classical solutions\, which leads to
the concept of semi-uniform stability. Specifically\, if all classical so
lutions decay at a polynomial rate\, the system is called polynomially sta
ble. This presentation aims to introduce the notions of semi-uniform ISS/i
ISS and its subclass\, polynomial ISS/iISS\, for infinite-dimensional syst
ems. I characterize semi-uniform ISS by attractivity properties and discus
s polynomial ISS of linear systems and polynomially iISS of bilinear syste
ms.\n\n**Biography:** \nMasashi Wakaiki received the B.S. degree in Eng
ineering and the M.S. and Ph.D. degrees in Informatics from Kyoto Universi
ty\, Kyoto\, Japan\, in 2010\, 2012\, and 2014\, respectively. He was a vi
siting scholar at the University of California\, Santa Barbara from 2014 t
o 2016. He was an Assistant Professor in the Department of Electrical and
Electronic Engineering\, Chiba University from 2016 to 2017. He was a Lect
urer in the Graduate School of System Informatics\, Kobe University from 2
017 to 2020\, where he is currently an Associate Professor. His research i
nterests include infinite-dimensional systems and networked control system
s.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Angeli (Imperial College London\, UK)
DTSTART;VALUE=DATE-TIME:20230712T150000Z
DTEND;VALUE=DATE-TIME:20230712T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/25
DESCRIPTION:Title: Input-to-State Stability for Complex Dynamics\nby David Angeli (Im
perial College London\, UK) as part of Input-to-State Stability and its Ap
plications\n\n\nAbstract\nTraditional ISS is formulated for systems global
ly defined on Euclidean space with a single equilibrium corresponding to t
he unperturbed system (0 input disturbance). This limits its applicability
to many other domains\, where multiple equilibria exists\, or more exotic
attractors (such as periodic solutions) or even multiple invariant sets o
f different nature.\nIn this talk we provide an extension of the definitio
ns and main results of ISS to this more general set-up\, arguing that a ve
ry natural extension of all the concepts is possible\, including asymptoti
c gain formulations and Lyapunov characterizations.\n\n**Biography:** \
nDavid Angeli received the B.S. degree in Computer Science Engineering and
the Ph.D. degree in Control Theory from University of Florence\, Florence
\, Italy\, in 1996 and 2000\, respectively.\nSince 2000\, he was with the
Department of Systems and Computer Science\, University of Florence\, as a
n Assistant Professor\, and an Associate Professor\, in 2005. In 2007\, he
was a Visiting Professor with I.N.R.I.A de Rocquencourt\, Paris\, France\
, and he joined as a Senior Lecturer the Department of Electrical and Elec
tronic Engineering\, Imperial College London\, London\, U.K.\, in 2008\, w
here he is currently a Professor in Nonlinear Network Dynamics and the Dir
ector of the MSc in Control and Optimisation. He has authored more than 10
0 journal papers in the areas of stability of nonlinear systems\, control
of constrained systems (MPC)\, chemical reaction networks theory\, and sma
rt grids.\nProf Angeli is a Fellow of IEEE (2015) and of the Institute of
Engineering and Technology (IET)\, since 2018. He has served as an Associa
te Editor for IEEE Transactions in Automatic Control and Automatica.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emilia Fridman (Tel Aviv University\, Israel)
DTSTART;VALUE=DATE-TIME:20230726T150000Z
DTEND;VALUE=DATE-TIME:20230726T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/26
DESCRIPTION:Title: Extremum seeking via a time-delay approach to averaging\nby Emilia
Fridman (Tel Aviv University\, Israel) as part of Input-to-State Stabilit
y and its Applications\n\n\nAbstract\nExtremum Seeking (ES) is a powerful
real-time optimization method without requesting a knowledge of system mod
el. A majority of ES algorithms employ highly oscillating dithers\, where
the stability analysis is based on the averaging theory. However\, the exi
sting results on averaging are qualitative: the original system is stable
for small enough values of the parameter if the averaged system is stable.
By using these results it is difficult to find an efficient bound on the
dither frequency that preserves the stability of the original system.\n\n
\n\nIn this talk I will present a new constructive time-delay approach to
averaging and apply it to ES.\n\nGradient-based ES of quadratic static map
s via the classical and bounded ES algorithms will be considered. The prac
tical stability analysis will be based on the transformation of the ES sys
tem to a time-delay one\, where the delay is defined by the dither frequen
cy. The results will be extended to sampled-data and delayed implementatio
ns.\n\nThe time-delay approach leads to quantitative bounds on the ES para
meters for the ''grey box" models and explicit qualitative bounds for the
''black box" models making ES control reliable.\n\nThese are joint results
with my recent post-docs Yang Zhu (Zhejiang University)\, Jin Zhang (Shan
ghai University) and Xuefei Yang (Harbin Institute of Technology).\n\n**B
iography:**\nEmilia Fridman received the M.Sc and Ph.D in mathematics in
Russia. Since 1993 she has been at Tel Aviv University\, where she is cur
rently Professor in the Department of Electrical Engineering - Systems. Sh
e has held numerous visiting positions in Europe\, China and Australia. He
r research interests include time-delay systems\, networked control system
s\, distributed parameter systems\, robust control and extremum seeking. S
he has published more than 200 journal articles and 2 monographs.\n\nIn 20
21 she was recipient of IFAC Delay Systems Life Time Achievement Award and
of Kadar Award for outstanding research in Tel Aviv University. In 2023 h
er monograph\n\n``Introduction to Time-Delay Systems: Analysis and Control
" (Birkhauser\, 2014) was the winner of IFAC Harold Chestnut Control Engin
eering Textbook Prize.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Chaillet (L2S Paris-Saclay\, France)
DTSTART;VALUE=DATE-TIME:20230719T150000Z
DTEND;VALUE=DATE-TIME:20230719T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/27
DESCRIPTION:Title: ISS for delay systems: an overview and some open questions\nby Ant
oine Chaillet (L2S Paris-Saclay\, France) as part of Input-to-State Stabil
ity and its Applications\n\n\nAbstract\nThis talk provides an overview of
the input-to-state stability (ISS) framework for nonlinear time-delay syst
ems. It aims at underlying the key differences existing with respect to bo
th the finite-dimensional theory and the general infinite-dimensional sett
ing. This overview covers fundamental properties of time-delay systems (in
cluding forward completeness and bounded reachability)\, input-free stabil
ity properties (including asymptotic and exponential stability)\, and ISS-
related notions (including integral ISS). All these properties will be dis
cussed at the light of both solutions-based and Lyapunov-based characteriz
ations. It will insist on some open questions that remain in the field to
hopefully foster some discussion. This work is mostly based on a collabora
tion with I. Karafyllis\, P. Pepe and Y. Wang\, and particularly on our re
cent survey paper "The ISS framework for time-delay systems: a survey" wri
tten at the occasion of E.D. Sontag's 70th birthday.\n\n**Biography:**
\nAntoine Chaillet was born in Douai\, France\, in 1979. He received his B
.Sc. degree from ESIEE Amiens\, France\, and his M.Sc. degree in Control E
ngineering from Univ. Paris Sud 11. In 2006\, he received his Ph.D. degree
in Control Theory from Univ. Paris Sud. In 2006–2007\, he served as a p
ost-doc fellow at Centro di Ricerca Piaggio\, Pisa\, Italy. From 2007 to 2
016\, he served as an associate professor at L2S-Univ. Paris Sud-Supélec.
He is now full professor at CentraleSupélec and former junior member of
Institut Universitaire de France. His research interests include stability
analysis and stabilization of nonlinear systems\, time-delay systems\, an
d control theory for neuroscience applications.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrii Mironchenko (University of Passau\, Germany)
DTSTART;VALUE=DATE-TIME:20230802T150000Z
DTEND;VALUE=DATE-TIME:20230802T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/28
DESCRIPTION:Title: Robust forward completeness: a bridge between well-posedness and stabi
lity.\nby Andrii Mironchenko (University of Passau\, Germany) as part
of Input-to-State Stability and its Applications\n\n\nAbstract\nWell-posed
ness theory studies the existence and uniqueness of solutions of dynamical
and control systems\, but it does not tell us much about the bounds of so
lutions. \nIn contrast to that\, the stability theory investigates the glo
bal in time bounds for trajectories and families of trajectories.\n\nWe kn
ow a lot about well-posedness and stability. But what do we know about the
terrain between these areas? In this talk\, I invite you to go with me to
these rather unexplored lands\, and summarize what we know about 2 relate
d concepts: robust forward completeness (RFC) and boundedness of reachabil
ity sets (BRS).\n\nRFC/BRS are important in many contexts:\n\n1. They were
instrumental for the derivation of converse Lyapunov theorems for global
asymptotic stability in ODE setting. \n\n2. Uniform global asymptotic stab
ility for infinite-dimensional systems has been characterized in terms of
uniform weak attractivity\, local stability\, and RFC property. \n\n3. Inp
ut-to-state stability (ISS) is equivalent to a combination of the uniform
limit property\, local stability\, and boundedness of reachability sets (s
o-called ISS superposition theorem). \n\n4. These characterizations\, in t
urn\, paved the way for the development of non-coercive Lyapunov methods\,
where again BRS/RFC play an important role.\n\n5. Characterization of glo
bal asymptotic stability for retarded systems is heavily dependent on whet
her the systems are RFC. \n\n6. BRS/RFC help significantly to study regula
rity of the flow of nonlinear infinite-dimensional control systems.\n\nAnd
now more formally:\n\nA control system is called forward complete if for
any initial condition $x$\, and any input $u$\, the corresponding trajecto
ry $\\phi(\\cdot\,x\,u)$ is well-defined on the whole nonnegative time axi
s. If additionally\, for any magnitude $R>0$ and any time $\\tau>0$\n\\[\n
\\sup_{\\|x\\| \\leq R\,\\ u\\in D\,\\ t\\in[0\,\\tau]} \\|\\phi(t\,x\,u)\
\| <+\\infty\,\n\\] \nwhere $D$ is the space of admissible inputs\, then a
control system is said to be robustly forward complete (RFC).\n\nWe start
by recalling the well-known result that forward completeness is equivalen
t to RFC for ODE systems with Lischitz right-hand side. We demonstrate by
means of an example\, that RFC is a stronger notion for infinite-dimension
al systems in Hilbert spaces with Lipschitz continuous rhs. \n\nWe show th
at the robust forward completeness for distributed parameter systems is eq
uivalent to the existence of a corresponding Lyapunov function that increa
ses at most exponentially along the trajectories.\n\nWe demonstrate severa
l results showing importance of RFC and BRS concepts. \nFinally\, we state
several open problems in this area.\n\n**Biography:**\nAndrii Mironche
nko was born in 1986 in Odesa\, Ukraine. He received the M.Sc. degree in
applied mathematics from the Odesa I.I. Mechnikov National University\, Od
esa\, Ukraine\, in 2008\, the Ph.D. degree in mathematics from the Univers
ity of Bremen\, Bremen\, Germany in 2012\, and the habilitation degree fr
om the University of Passau\, Germany\, in 2023. He has held a research po
sition with the University of Würzburg\, Würzburg\, Germany\, and was a
Postdoctoral Fellow of Japan Society for Promotion of Science (JSPS) with
the Kyushu Institute of Technology\, Fukuoka Prefecture\, Japan (2013–20
14). Since 2014\, he is with the Faculty of Mathematics and Computer Scien
ce\, University of Passau\, Passau\, Germany.\n\nDr. Mironchenko is the au
thor of the monograph „Input-to-State Stability“ (Springer\, 2023) and
(co)author of more than 60 peer-reviewed papers in journals and conferenc
e proceedings in control theory and applied mathematics. \nA. Mironchenko
is a co-founder and co-organizer of the Workshop series “Stability and C
ontrol of Infinite-Dimensional Systems” (SCINDIS). He is a Senior Member
of IEEE.\n\nHis research interests include stability theory\, nonlinear s
ystems theory\, distributed parameter systems\, hybrid systems\, and appli
cations of control theory to biological systems and distributed control.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iasson Karafyllis (National Technical University of Athens)
DTSTART;VALUE=DATE-TIME:20231018T150000Z
DTEND;VALUE=DATE-TIME:20231018T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/29
DESCRIPTION:Title: Let’s Use Delays in Adaptive Control!\nby Iasson Karafyllis (Nat
ional Technical University of Athens) as part of Input-to-State Stability
and its Applications\n\n\nAbstract\nThis talk shows the first step towards
the resolution of several decades-old challenges in disturbance-robust ad
aptive control. For a scalar\, delay-free\, linear system with an unknown
parameter for which no a priori bound is given\, with a disturbance that i
s of unlimited magnitude and possibly persistent (not square integrable)\,
and without a persistency of excitation necessarily verified by the state
\, the problem of (practical) Input-to-Output Stability (IOS) asymptotic g
ain assignment relative to the disturbance is studied. A solution to these
heretofore unsolved feedback design problems is provided with the aid of
infinite-dimensional nonlinear feedback employing distributed delay of the
state and input itself. Specifically\, in addition to (0) global boundedn
ess of the infinite-dimensional state of the closed-loop system when the d
isturbance is present\, the following features are also established: (1) p
ractical IOS with assignable asymptotic gain from the disturbance to the p
lant state\; (2) assignable exponential convergence rate\; and (3) assigna
ble radius of the residual set. The accompanying identifier in the propose
d adaptive control scheme guarantees (4) boundedness of the parameter esti
mate even when disturbances are present\; (5) an ultimate estimation error
which is proportional to the magnitude of the disturbance with assignable
gain when there exists sufficient excitation of the state\; and (6) exact
parameter estimation in finite-time when the disturbance is absent and th
ere is sufficient excitation. Among the obtained results\, one reveals a t
radeoff between “learning capacity” and “disturbance robustness:”
the less sensitive the identifier is to the disturbance\, the less likely
it is to learn the parameter. This is a joint work with Miroslav Krstic an
d Alexandros Aslanidis. \n\n**Biography: **\nIasson Karafyllis is a
Professor of Mathematics in the Department of Mathematics of the National
Technical University of Athens. He is a coauthor of three books and he ha
s written more than 100 journal papers. His research interests lie in the
stability theory and feedback stabilization theory of deterministic contro
l systems as well as in the connection of Mathematical Control Theory with
other areas of mathematics.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Schwenninger (University of Twente\, Netherlands)
DTSTART;VALUE=DATE-TIME:20231108T160000Z
DTEND;VALUE=DATE-TIME:20231108T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/30
DESCRIPTION:Title: BIBO stability and ISS for infinite-dimensional systems\nby Felix
Schwenninger (University of Twente\, Netherlands) as part of Input-to-Stat
e Stability and its Applications\n\n\nAbstract\nIn this talk we revisit Bo
unded-input-bounded-output (BIBO) stability for infinite-dimensional syste
ms. We discuss subtleties arising even in the linear case and its relation
s to ISS. The focus is on phenomena arising from boundary control and obse
rvation.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jun Zheng (Southwest Jiaotong University\, Chengdu\, PR China)
DTSTART;VALUE=DATE-TIME:20231025T150000Z
DTEND;VALUE=DATE-TIME:20231025T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/31
DESCRIPTION:Title: ISS for the Burgers’ Equation with Dirichlet Boundary Disturbances a
nd the Generalized Lyapunov Method\nby Jun Zheng (Southwest Jiaotong U
niversity\, Chengdu\, PR China) as part of Input-to-State Stability and it
s Applications\n\n\nAbstract\nThe input-to-state stability (ISS) theory of
partial differential equations (PDEs) has been developed for more than on
e decade. During this period\, a few methods have been proposed for establ
ishing the ISS for PDEs subjected to distributed in-domain disturbances an
d various types of boundary disturbances. In particular\, the Lyapunov met
hod has proven to be well-suited to PDEs with solely in-domain disturbance
s or boundary disturbances of Robin and Neumann types. However\, applying
the Lyapunov arguments the ISS analysis of PDEs with Dirichlet boundary di
sturbances meets a significant challenge.\n\nIn this presentation\, we wil
l first illustrate how to construct Lyapunov-like functionals to achieve t
he ISS in different norms for the Burgers’ equation with Dirichlet bound
ary disturbances. Unlike classical Lyapunov functionals\, which are typica
lly required to be positive definite\, these constructed Lyapunov-like fun
ctionals can be positive semidefinite. Furthermore\, such functionals are
allowed to be depend on the boundary disturbances. As a result\, this kind
of construction provides a wider range of choices for the ISS-Lyapunov ca
ndidates and offers greater flexibility in applications.\n\nInspired by st
udying the ISS for the Burgers’ equation\, we will then show how to exte
nd the proposed approach to general infinite-dimensional systems. In parti
cular\, we will introduce a new notion called the generalized ISS-Lyapunov
functional (GISS-LF) by using positive semidefinite and disturbance-depen
dent functionals. We will also present a generalized ISS-Lyapunov theorem\
, indicating that the existence of a GISS-LF implies the ISS of the consid
ered system. Consequently\, the proposed approach can be seen as a general
ized Lyapunov method\, providing a new perspective for the ISS analysis of
infinite dimensional systems including PDEs with Dirichlet boundary distu
rbances. \n\nThis is a joint work with Prof. Guchuan Zhu from Polytechniqu
e Montreal.\n\n**Biography: **\nJun Zheng received the Ph.D. degree in
mathematics from Lanzhou University\, Lanzhou\, China\, in 2013. He joined
Southwest Jiaotong University\, Chengdu\, China\, in 2013\, where he is c
urrently an associate professor at the School of Mathematics. He has publi
shed more than 40 papers by peer-reviewed journals in the fields of contro
l and mathematics. His current research interests include control of distr
ibuted parameter systems\, nonlinear and robust control\, free boundary pr
oblems\, and regularity theory of PDEs.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolás Espitia (University of Lille - CNRS - CRIStAL laboratory\
, France)
DTSTART;VALUE=DATE-TIME:20231122T160000Z
DTEND;VALUE=DATE-TIME:20231122T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/32
DESCRIPTION:Title: Event-triggered boundary control of an unstable reaction diffusion PDE
with input delay\nby Nicolás Espitia (University of Lille - CNRS - C
RIStAL laboratory\, France) as part of Input-to-State Stability and its Ap
plications\n\n\nAbstract\nEvent-triggered control has gained significant a
ttention within the control community and has already reached a certain le
vel of maturity within the framework of finite-dimensional networked contr
ol systems. However\, when it comes to infinite-dimensional systems\, spec
ifically partial differential equations (PDEs)\, this area remains in its
early stages. Event-triggered control for PDEs presents a multitude of cha
llenging issues\, including those theoretical ones related to well-posedne
ss\, the occurrence of the Zeno phenomenon\, and conservatism\, among othe
rs. The emergence of these challenges depends on various factors\, such as
the nature of the PDE (e.g.\, whether hyperbolic or parabolic)\, the way
for sensing and actuation (in-domain or boundary)\, the design of the cont
rol methodology employed\, and the intended applications while modeling by
a PDE setting.\n\nThis presentation will focus on recent advancements in
event-triggered boundary control applied to a specific class of 1-dimensio
nal reaction-diffusion PDE with delayed boundary input. The discussion wil
l start by providing some fundamental elements of event-triggered control
and illustrative examples where event-triggered control can play a fundame
ntal role\, particularly in PDE control\, as this strategy can represent a
more realistic and practical means of actuating PDE systems.\nSubsequentl
y\, this talk will introduce an event-triggered boundary control strategy
of reaction -diffusion PDEs for the delay-free case. This result is crucia
l in preparing the basis for the extension to cases involving input delays
. Our methodology builds on well-established and powerful control design t
echniques for PDEs\, such as the backstepping approach\, as well as insigh
ts from Input-to-State Stability (ISS) results for PDEs and small-gain arg
uments. The presentation will highlight the employed event-triggering poli
cy (using suitable spatial norms)\, the stability results\, and how we can
avoid the Zeno phenomenon.\nThis work is mostly based on a recent collabo
ration with Miroslav Krstic and Florent Koudohode.\n\n**Biography: **\n
Nicolas Espitia is a researcher at the CNRS (The National Center for Scien
tific Research) since 2019 and develops his research activities within the
CRIStAl laboratory (Research Center in Computer Science\, Signal and Auto
matic Control of Lille) of the University of Lille\, France. \nHe received
in 2017 his Ph.D. in Control Systems from the GIPSA-Lab\, University of
Grenoble\, France. From 2017 to 2019\, he was a postdoctoral researcher in
Inria Lille Nord-Europe\, France. His research interests include event-tr
iggered control and finite-/fixed-/prescribed-time stabilization of infini
te-dimensional systems.\n\n**References: **\n\n-N. Espitia\; I. Karafyl
lis\; M. Krstic "Event-triggered boundary control of constant-parameter r
eaction-diffusion PDEs: A small-gain approach"\, Automatica\, Vol. 128\, 2
021 (Doi: https://doi.org/10.1016/j.automatica.2021.109562\; HAL: https://
hal.science/hal-03178456)\n\n-F. Koudohode\; N Espitia\; M. Krstic\, "Even
t-triggered boundary control of an unstable reaction diffusion PDE with in
put delay"\, under review in Systems & Control Letters (preprint avialable
at HAL: https://hal.science/hal-04304378 ).\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maurice Heemels (Eindhoven University of Technology\, Netherlands)
DTSTART;VALUE=DATE-TIME:20231129T160000Z
DTEND;VALUE=DATE-TIME:20231129T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/33
DESCRIPTION:Title: Projected Dynamics in Control\nby Maurice Heemels (Eindhoven Unive
rsity of Technology\, Netherlands) as part of Input-to-State Stability and
its Applications\n\n\nAbstract\nProjected Dynamical Systems (PDSs) are a
class of discontinuous and constrained dynamical systems in which projecti
on of dynamics is used to keep the state of the system in a given constrai
nt set. In this talk we will focus on the opportunities that PDS may offer
for high-performance control purposes. In particular\, we will consider t
he utilization of projection operators in control systems to overcome fund
amental performance limitations related to linear time-invariant (LTI) con
trol. As an exemplary controller\, we will discuss the so-called Hybrid I
ntegrator-Gain System (HIGS)\, being a projected integrator designed to av
oid the limitations of linear integrators. The main design philosophy behi
nd HIGS is built on keeping the sign of its input and output equal\, there
by inducing less phase lag than a linear integrator\, which leads to direc
t performance benefits. The study of HIGS calls for an extension of classi
cal PDS (called “extended PDS”)\, as only partial projection of the cl
osed-loop states is allowed\; we can only change the controller states by
projection\, not the plant states. This novel use of projection operators
can enforce desirable input-output (i/o) properties of the controller dyna
mics\, which were not present in the original (unprojected) dynamics. In f
act\, we will show\, for instance\, how next to sign-equivalence properti
es of inputs and outputs\, also passivity and general (qsr-)dissipativity
properties can be induced by projection on sector-like i/o constraint sets
. For the class of HIGS-controlled systems (and their formalizations in te
rms of ePDSs)\, we discuss existence and forward completeness of solutions
\, their discretizations and sampled-data implementations\, and (input-to-
state and incremental) stability properties and illustrate them by various
examples and experiments. \n\n**Biography: **\nMaurice Heemels receiv
ed M.Sc. (mathematics) and Ph.D. (control theory) degrees (summa cum laude
) from the Eindhoven University of Technology (TU/e) in 1995 and 1999\, re
spectively. From 2000 to 2004\, he was with the Electrical Engineering Dep
artment\, TU/e\, as an assistant professor\, and from 2004 to 2006 with th
e Embedded Systems Institute (TNO-ESI) as a research fellow. Since 2006\,
he has been with the Department of Mechanical Engineering\, TU/e\, where h
e is currently a Full Professor and vice-dean. Maurice held visiting profe
ssor positions at Swiss Federal Institute of Technology (ETH)\, Switzerla
nd (2001)\, University of California at Santa Barbara (2008) and Universit
y of Lorraine\, France (2020). His current research includes hybrid and cy
ber-physical systems\, networked and event-triggered control systems and m
odel predictive control. Dr. Heemels served/s on the editorial boards of A
utomatica\, Nonlinear Analysis: Hybrid Systems\, Annual Reviews in Contro
l\, and IEEE Transactions on Automatic Control. He was a recipient of a pe
rsonal VICI grant awarded by NWO (Dutch Research Council) and an ERC Advan
ced Grant (European Research Council). He is a Fellow of the IEEE and IFAC
. He was currently chair of the IFAC Technical Committee on Networked Sys
tems (2017-2023). He was the recipient of the 2019 IEEE L-CSS Outstanding
Paper Award and the 2020 Automatica Paper Prize Award. He was elected for
the IEEE-CSS Board of Governors (2021-2023). He is the Editor-in-Chief of
the IFAC journal Nonlinear Analysis: Hybrid Systems as of 2023.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Delphine Bresch-Pietri (MINES ParisTech\, France)
DTSTART;VALUE=DATE-TIME:20231206T160000Z
DTEND;VALUE=DATE-TIME:20231206T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/34
DESCRIPTION:Title: Input-to-State Stability and converse Lyapunov Theorem for Linear Diff
erence Equations and Hyperbolic Partial Differential Equations\nby Del
phine Bresch-Pietri (MINES ParisTech\, France) as part of Input-to-State S
tability and its Applications\n\n\nAbstract\nIn this talk\, we will focus
on a specific type of time-delay systems\, namely\, linear difference equa
tions\, which are seldom studied in the literature. We will review their s
trong connection with systems of Linear Hyperbolic Partial Differential Eq
uations and the corresponding control challenges. We will present some con
texts of hyperbolic PDEs in which stabilizing control laws could be design
ed via the reformulation of the dynamics by means of a difference equation
. We will also present how this reformulation could be used to express a c
onverse Input-to-State Stability Lyapunov theorem for systems of hyperboli
c PDEs. This talk is inspired from recent works with Jean Auriol (CNRS\, L
2S).\n\n**Biography: **\nDelphine Bresch-Pietri is an Associate Profess
or at Mines Paris - PSL\, at the Centre d'Automatique et Systèmes. Her re
search areas include the theory and applications of time-delay systems\, b
oundary control of Partial Differential Equations\, and optimization of ti
me-delay systems. She is the co-author of a control engineering book title
d "Stabilité et Stabilisation" and holds several patents in the field of
engine control. She has been an Associate Editor at Systems and Control Le
tters since 2020 and at IEEE Transactions on Automatic Control since 2022.
\n\n**References: **\n\n-Jean Auriol\, Delphine Bresch-Pietri. On Input
-to-State Stability of Linear Difference Equations and\nIts Characterizati
on with a Lyapunov Functional. IFAC World Congress 2023\nhttps://hal.scien
ce/hal-04051122/document\n\n-Auriol Jean\, Kong Sijia\, and Bresch-Pietri
Delphine. "Explicit prediction-based control for linear difference equatio
ns with distributed delays." IEEE Control Systems Letters 6 (2022): 2864-2
869.\nhttps://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=9786057\n\n-Jea
n Auriol and Delphine Bresch Pietri. "Robust state-feedback stabilization
of an underactuated network of interconnected n+ m hyperbolic PDE systems.
" Automatica 136 (2022): 110040.\nhttps://www.sciencedirect.com/science/ar
ticle/pii/S0005109821005689\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hernan Haimovich (Universidad Nacional de Rosario (UNR) and Consej
o Nacional de Investigaciones Científicas y Técnicas (CONICET)\, Argenti
na)
DTSTART;VALUE=DATE-TIME:20231115T160000Z
DTEND;VALUE=DATE-TIME:20231115T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/35
DESCRIPTION:Title: Forward Completeness is not robust for time-delay Systems: Intuition\,
counterintuition and consequences\nby Hernan Haimovich (Universidad N
acional de Rosario (UNR) and Consejo Nacional de Investigaciones Científi
cas y Técnicas (CONICET)\, Argentina) as part of Input-to-State Stability
and its Applications\n\n\nAbstract\nForward Completeness (FC) is the prop
erty indicating that solutions of a dynamical system are defined for all f
uture times. For ODEs that represent time-invariant dynamical systems with
inputs\, standard assumptions cause FC to be equivalent to Robust FC (RFC
)\, the latter meaning that solutions originating in bounded balls and cor
responding to inputs taking values in a compact set have uniform bounds ov
er compact time intervals. The equivalence between FC and RFC ceases to ho
ld for infinite-dimensional systems\, but the validity of this equivalence
for the specific case of time-delay systems has until recently been an op
en question. In this talk\, it will be shown that the FC and RFC of usuall
y encountered classes of time-delay systems are related to the FC of ODEs
under different sets of admissible inputs: continuous inputs for FC and me
asurable and locally essentially bounded inputs for RFC. The existence of
an FC time-delay system whose related ODE system is FC for continuous inpu
ts but not for all bounded measurable inputs is shown with an interesting
example from the realm of switched systems. This shows that FC is not equi
valent to RFC for time-delay systems. The perhaps counterintuitive propert
ies of the constructed example will be examined and the corresponding cons
equences indicated. This talk ends by pointing to some problems that may s
till remain open regarding the relationship between FC and RFC for general
time-delay systems. This is joint work with Prof. Jose Luis Mancilla-Agui
lar.\n\n**Biography: **\nHernan Haimovich graduated as an Electronics E
ngineer in 2001 at the Universidad Nacional de Rosario (UNR)\, Argentina\,
and finished his Ph.D. at The University of Newcastle\, Australia\, in 20
06. Dr. Haimovich currently holds a permanent Investigator position from C
ONICET (the national research council of Argentina) and is a Professor at
the School of Electronics Engineering\, UNR. Dr. Haimovich is highly enthu
siastic about applied mathematics in relation to control systems. His rese
arch interests include control theory for nonlinear\, switched\, time-vary
ing\, impulsive\, hybrid and/or discontinuous systems\, and related applic
ations.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergiy Zhuk (IBM Research Europe\, Dublin\, Ireland)
DTSTART;VALUE=DATE-TIME:20240110T160000Z
DTEND;VALUE=DATE-TIME:20240110T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/36
DESCRIPTION:Title: Simulation-friendly detectability and ISS conditions for turbulent Nav
ier-Stokes equations with unknown inputs\nby Sergiy Zhuk (IBM Research
Europe\, Dublin\, Ireland) as part of Input-to-State Stability and its Ap
plications\n\n\nAbstract\nWe will present simulation friendly detectabilit
y and ISS conditions for 2D Navier–Stokes Equation (NSE) with periodic b
oundary conditions\, and describe a generic class of ‘‘detectable’
’ observation operators: it includes pointwise evaluation of NSE’s sol
ution at interpolation nodes\, and spatial average measurements. Our anal
ysis relies upon a novel one-parametric inequality relating $L^\\infty$ an
d $H^2$-norms of periodic vector-functions\, which for certain values of t
he parameter reduces to Agmon and Brezis inequalities\, and S-procedure wi
dely used in Lyapunov stability analysis.\n\nWe show that the solution of
NSE for an unknown initial condition for $\\vec a$ destabilizing unknown
input belongs to $H^1$-ellipsoid which shrinks provided the uncertain inpu
t ‘‘perturbs’’ the system less and less frequently as $t \\to \\in
fty$\, or $L^2$-norm of this perturbation (in space) decays as $t \\to \\i
nfty$\, a remarkable result for turbulent systems which are highly sensiti
ve to small perturbations. \n\nFor ‘‘detectable’’ observation ope
rators we design a global infinite-dimensional observer for NSE with uncer
tain possibly destabilizing inputs: in our numerical experiments we illust
rate $H^1$-sensitivity of NSE to small perturbations of initial conditions
\, yet the observer converges for known and uncertain inputs.\n\n**Biogra
phy: **\nSergiy Zhuk is a Senior Research Scientist at IBM Research Euro
pe\, and he is a manager of the Quantum Computing group based in Dublin\,
Ireland. Sergiy holds a Ph.D. in Applied Mathematics from Taras Shevchenko
National University of Kyiv\, Ukraine. In 2009 Sergiy was granted an ERCI
M/Marie Curie fellowship with Centrum Wiskunde Informatica (The Netherland
s) and INRIA Paris-Rocquencourt research center (France). Sergiy has been
a visiting scholar at Inria Paris research center and Mathematical institu
te of Utrecht University. He joined IBM Research Europe in 2012. In 2016
–2019 he was an\nadjunct assistant professor at University College Dubli
n. His research interests include state and parameter estimation for dynam
ical systems\, inverse modeling\, Markov decision processes and (more rece
ntly) quantum computing.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Müller (Leibniz University Hannover\, Germany)
DTSTART;VALUE=DATE-TIME:20240124T160000Z
DTEND;VALUE=DATE-TIME:20240124T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/38
DESCRIPTION:Title: Incremental input/output-to-state stability and its application in the
analysis and design of optimization-based state estimators\nby Matthi
as Müller (Leibniz University Hannover\, Germany) as part of Input-to-Sta
te Stability and its Applications\n\n\nAbstract\nThe notion of incremental
input/output-to-state stability (i-IOSS) was originally proposed by Sonta
g and Wang in 1997. It constitutes an extension of zero-detectability (whi
ch is implied by IOSS) to arbitrary trajectories and entails an asymptotic
distinguishability property of states involving past input/output data. M
oreover\, it can be interpreted as robust generalization of standard (fina
l state) observability for systems with unobservable\, asymptotically deca
ying modes that are subject to process disturbances and measurement noise\
, and i-IOSS was even shown to be a necessary and sufficient property for
the existence of robustly stable state estimators. In the first part of th
is talk\, we discuss how recently developed converse Lyapunov theorems for
finite dimensional (discrete- and continuous-time) systems establish equi
valence of i-IOSS and existence of an exponential-decrease i-IOSS Lyapunov
function. Furthermore\, we show how the strong relation to contraction th
eory enables the application of straightforward tools to check exponential
i-IOSS in practice using quadratically bounded i-IOSS Lyapunov functions.
\n\nIn recent years\, i-IOSS has become the standard assumption of nonline
ar detectability in the context of optimization-based state estimation for
discrete-time systems\, in particular\, moving horizon estimation (MHE).
This technique is naturally applicable to nonlinear\, potentially constrai
ned systems and has applications in various fields\, such as chemical and
process engineering\, biomedical engineering and systems medicine\, roboti
cs\, and power systems. In the second part of this talk\, we show how stro
ng robustness guarantees can be provided for MHE under i-IOSS when the MHE
cost function is chosen in accordance with the parameters of the i-IOSS L
yapunov function. In particular\, this leads to practically relevant condi
tions for the design of nonlinear MHE schemes.\n\n**Biography: **\n Mat
thias A. Müller received a Diploma degree in Engineering Cybernetics from
the University of Stuttgart\, Germany\, an M.Sc. in Electrical and Comput
er Engineering from the University of Illinois at Urbana-Champaign\, US (b
oth in 2009)\, and a Ph.D. from the University of Stuttgart in 2014. Since
2019\, he is director of the Institute of Automatic Control and full prof
essor at the Leibniz University Hannover\, Germany. His research interests
include nonlinear control and estimation\, model predictive control\, and
data- and learning-based control\, with applications in different fields
including biomedical engineering and robotics. He has received various awa
rds for his work\, including the 2015 European Systems & Control PhD Thesi
s Award\, the inaugural Brockett-Willems Outstanding Paper Award for the b
est paper published in Systems & Control Letters in the period 2014-2018\,
an ERC starting grant in 2020\, the IEEE CSS George S. Axelby Outstanding
Paper Award 2022\, and the Journal of Process Control Paper Award 2023. H
e serves as associate editor for Automatica\, editor of the International
Journal of Robust and Nonlinear Control\, and as a member of the Conferenc
e Editorial Board of the IEEE Control Systems Society.\n\n**Related refer
ences: **\n\n-Sven Knüfer and Matthias A. Müller (2018).\n"Robust Glob
al Exponential Stability for Moving Horizon Estimation".\nProc. IEEE Conf.
Decis. Control 2018\, p. 3477-3482.\nhttps://ieeexplore.ieee.org/document
/8619617\n\n-Sven Knüfer and Matthias A. Müller (2020).\n"Time-Discounte
d Incremental Input/Output-to-State Stability".\nProc. IEEE Conf. Decis. C
ontrol 2020\, p. 5394-5400.\nhttps://ieeexplore.ieee.org/document/9304034\
n\n-Sven Knüfer and Matthias A. Müller (2023).\n"Nonlinear full informat
ion and moving horizon estimation: Robust global asymptotic stability".\nA
utomatica 150\, p. 110603.\nhttps://www.sciencedirect.com/science/article/
abs/pii/S0005109822004654?via%3Dihub\n\n-Julian D. Schiller and Matthias A
. Müller (2023).\n"On an integral variant of incremental input/output-to-
state stability and its use as a notion of nonlinear detectability".\nIEEE
Contr. Syst. Lett. 7\, p. 2341-2346.\nhttps://ieeexplore.ieee.org/documen
t/10153397\n\n-Julian D. Schiller and Matthias A. Müller (2023).\n"Robust
stability of moving horizon estimation for continuous-time systems".\narX
iv:2305.06614.\nhttps://arxiv.org/abs/2305.06614\n\n-Julian D. Schiller\,
Simon Muntwiler\, Johannes Köhler\, Melanie N. Zeilinger\, and Matthias A
. Müller (2023).\n"A Lyapunov function for robust stability of moving hor
izon estimation".\nIEEE Trans. Autom. Control 68(12)\, p. 7466-7481.\nhttp
s://ieeexplore.ieee.org/document/10136787\n\n-Julian D. Schiller and Matth
ias A. Müller (2023).\n"Suboptimal nonlinear moving horizon estimation".\
nIEEE Trans. Autom. Control 68(4)\, p. 2199-2214.\nhttps://ieeexplore.ieee
.org/document/9772349\n\n-Julian D. Schiller and Matthias A. Müller (2023
).\n"Nonlinear moving horizon estimation for robust state and parameter es
timation."\narXiv:2312.13175.\nhttps://arxiv.org/abs/2312.13175\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophie Tarbouriech (LAAS-CNRS\, Toulouse\, France)
DTSTART;VALUE=DATE-TIME:20240221T160000Z
DTEND;VALUE=DATE-TIME:20240221T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/39
DESCRIPTION:Title: Dynamic output feedback with adaptive saturation or dead-zone\nby
Sophie Tarbouriech (LAAS-CNRS\, Toulouse\, France) as part of Input-to-Sta
te Stability and its Applications\n\n\nAbstract\nIn this talk\, we discuss
the redesign of output feedback controllers (possible observer-like) for
linear systems based on adaptive saturation (stubborn) and dead-zone to im
prove noise reduction. With a stubborn redesign\, we improve the transient
response of the closed loop to measurement outliers. Instead\, with a dea
d-zone redesign\, we get a reduction in the sensitivity of the closed loop
to persistent disturbances such as measurement bias or Gaussian noise aff
ecting the output. Hence\, for any given stabilizing linear dynamic output
feedback law designed for a multivariable linear plant\, we provide LMI-b
ased stubborn/dead-zone redesign conditions that guarantee closed-loop exp
onential ISS. The feasibility of our LMI-based conditions is also proven.
\n\n**Biography: **\nSophie Tarbouriech received the Ph.D. and HDR degr
ees in Automatic Control from University Paul Sabatier\, Toulouse\, France
\, in 1991 and 1998\, respectively. She is full-time researcher (Directeu
r de Recherche CNRS) at LAAS-CNRS\, Toulouse. Her main research interests
include analysis and control of linear and nonlinear systems with constrai
nts (limited information)\, hybrid dynamical systems. She is currently Ass
ociate Editor for SIAM Journal on Control and Optimization and Senior Edit
or for IEEE Control Systems Letters. She is also Senior Editor and Deputy
Editor-in-Chief for Automatica. She is a member of International Federatio
n of Automatic Control and IEEE Technical Committees.\n\n **References: <
/b>\n\n- S. Tarbouriech\, A. Alessandri\, D. Astolfi and L. Zaccarian\, "L
MI-Based Stubborn and Dead-Zone Redesign in Linear Dynamic Output Feedback
\," in IEEE Control Systems Letters\, vol. 7\, pp. 187-192\, 2023\, doi: 1
0.1109/LCSYS.2022.3186842\, hal: hal-03726559.\n\n ****Slides: **\nhttp:/
/mironchenko.com/__My_php_sources/ISS-Seminar-Talks/2024-02-21-Tarbouriech
.pdf\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Brivadis (L2S\, CNRS\, University Paris Saclay\, France)
DTSTART;VALUE=DATE-TIME:20240214T160000Z
DTEND;VALUE=DATE-TIME:20240214T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/40
DESCRIPTION:Title: Forward completeness and bounded reachability sets for time-delay syst
ems: the role of the state space\nby Lucas Brivadis (L2S\, CNRS\, Univ
ersity Paris Saclay\, France) as part of Input-to-State Stability and its
Applications\n\n\nAbstract\nA dynamical system is forward complete (FC) if
its solutions are well-defined for all future times. If moreover solution
s initialized in bounded sets and corresponding to bounded inputs remain u
niformly bounded over bounded time-intervals\, then it is said to have the
bounded reachability sets (BRS) property\, also called robust forward com
pleteness (RFC). BRS is a bridge between the pure well-posedness theory (t
hat studies existence and uniqueness) and the stability theory (which is i
nterested in establishing certain bounds for solutions). For example\, BRS
is a crucial property to establish ISS superposition theorems. It is know
n that under standard assumptions\, FC implies BRS for finite-dimensional
systems\, while this fails for infinite-dimensional ones.\nIt was recently
shown by J.L. Mancilla-Aguilar and H. Haimovich that the implication also
fails in the case of time-delay systems with a finite number of delays. I
n this talk\, we aim to show that the implication FC => BRS for time-delay
systems actually heavily depends on the choice of the state space. In par
ticular\, we propose to consider the state space of essentially bounded fu
nctions (instead of the usual one of continuous functions). On this new st
ate space\, we prove that FC implies BRS\, which raises the question of re
visiting stability theory of time-delay systems in this state space.\n\n**Biography.** Lucas Brivadis is a CNRS researcher at the Laboratory of S
ignals and Systems (L2S\, CentraleSupélec\, CNRS\, Université Paris-Sacl
ay). He defended his PhD in 2021 at LAGEPP\, Université Lyon 1. From 2021
to 2022\, he was a postdoctoral researcher at L2S. His research interests
include stability properties of nonlinear delay systems\, observer design
for nonlinear or infinite dimensional systems\, and output feedback stabi
lization.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Wirth (University of Passau\, Germany)
DTSTART;VALUE=DATE-TIME:20240131T160000Z
DTEND;VALUE=DATE-TIME:20240131T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/41
DESCRIPTION:Title: The characterization of ISS for time-delay systems: Results and Counte
rexamples\nby Fabian Wirth (University of Passau\, Germany) as part of
Input-to-State Stability and its Applications\n\n\nAbstract\nWe consider
a general class of time-delay systems with inputs. While\nthis defines a c
lass of infinite-dimensional systems\, it has been\nobserved for a long ti
me that the analytic properties of such systems\nare more benign than in t
he general infinite-dimensional case. To give\nan example\, it is a classi
c result that for systems without input\nasymptotic stability of a fixed p
oint implies this property with a\nrate that is uniform in the state space
. As the state space is not\nlocally compact this is by no means as self-e
vident as for ODEs.\n\nOn the other hand it is also known that the infinit
e-dimensional\ncharater of time-delays systems results in properties that
are not\npossible for systems of ordinary differential equations. For inst
ance\,\nin a recent paper\, Mancilla-Aguilar and Haimovich have shown that
\nforward completeness does not imply boundedness of finite-time\nreachabi
lity sets (the BRS property\, for short). Even more strikingly\,\nthe exam
ple provided is even globally asymptotically stable and\nuniformly globall
y attractive in the fixed point zero.\n\nAll this touches upon the charact
erization of input-to-state stability\nfor time-delay systems in terms of
other dynamic properties of the\nsystem. The properties that have turned o
ut to be important are\n\nstability properties: (uniform) local stability
(LS/ULS)\,\nthe (uniform) limit property (LIM/ULIM)\, describing the long
term behaviour of trajectories\,\n(uniform) asymptotic gains (AG/UAG)\, de
scribing asymptotic bounds on trajectories.\n\nFor finite-dimensional cont
rol systems it has been shown by\nSontag and Wang that we have the equival
ence\n\nISS <=> LIM & LS <=> AG & LS\n\nIn contrast for a broad class of n
onlinear infinite-dimensional\nsystems it has been shown that stronger req
uirements are needed\, namely\,\n\nISS <=> ULIM & ULS & BRS <=> UAG & CEP
& BRS\n\nAnd in the context of the general infinite-dimensional class this
\ncharacterization cannot be relaxed. However\, delay systems are more\nbe
nign so that it possible to relax the characterization to\n\nISS <=> LIM &
0-ULS & BRS <=> AG & 0-ULS & BRS\n\nOn the other hand the example of Manc
illa-Aguilar and Haimovich may be\nextended to show that\, in the absence
of BRS\, LIM does not imply\nULIM. Also global asymptotic stability does n
ot imply uniform global\nattractivity. Thus the requirements on bounded re
achability\nsets and uniformity properties of the stability requirements c
annot be\nremoved in the time-delay case.\n\njoint work with\n\nLucas Briv
adis\, Université Paris-Saclay\, CNRS\, CentraleSupélec\, LSS\, France\,
\n\nAntoine Chaillet\, Université Paris-Saclay\, CNRS\, CentraleSupélec\
, LSS\, France\,\n\nAndrii Mironchenko\, University of Klagenfurt\, Austri
a and University of Passau\, Germany.\n\n**Biography.** \nFabian Wirth
received his PhD from the Institute of Dynamical Systems at\nthe Universit
y of Bremen in 1995. He has since held positions in Bremen\,\nat the Centr
e Automatique et Systèmes of Ecole des Mines\, the\nHamilton Institute at
NUI Maynooth\, Ireland\, the University of Würzburg and IBM Research Ire
land. \nHe now holds the chair for Dynamical Systems at the University\nof
Passau in Germany. His current interests include stability\ntheory\, swit
ched systems\, the joint spectral radius of matrix sets and large scale ne
tworks with \napplications to networked systems and distributed control.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrii Mironchenko (University of Klagenfurt\, Austria)
DTSTART;VALUE=DATE-TIME:20240117T160000Z
DTEND;VALUE=DATE-TIME:20240117T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/42
DESCRIPTION:Title: Revisiting Lyapunov-Krasovskii methodology for robust stability analys
is of time-delay systems\nby Andrii Mironchenko (University of Klagenf
urt\, Austria) as part of Input-to-State Stability and its Applications\n\
n\nAbstract\nLyapunov-Krasovskii functionals are a classical tool to study
asymptotic stability and \ninput-to-state stability of time-delay systems
. \nHowever\, in the ISS context\, the requirements on the Lyapunov-Krasov
skii functionals \nare much stronger than those used for analysis of asymp
totic stability. \n\nWhy? Can we fix it?\n\nIn this talk\, we show a Lyapu
nov-Krasovskii direct theorem\nfor ISS of time-delay systems. This\ntheore
m is valid for systems with mild regularity of the right-\nhand side and i
mposes fewer requirements on the Lyapunov-\nKrasovskii functional than the
known results. Finally\, we derive\na stronger property than classical IS
S.\nTo prove this result\, we introduce a new stability formalism\nfor del
ay systems with inputs and establish the \nISS superposition theorem speci
fically tailored for time-delay systems.\n\n**Biography.** Andrii Mi
ronchenko was born in 1986 in Odesa\, Ukraine. He received the Ph.D. degr
ee in mathematics from the University of Bremen\, Germany\, and the habili
tation degree from the University of Passau\, Germany. He was a Postdoctor
al Fellow of Japan Society for Promotion of Science (2013–2014). Since 2
023\, he is with the Department of Mathematics\, University of Klagenfurt
\, Austria.\n\nDr. Mironchenko is the author of the monograph „Input-to-
State Stability“ (Springer\, 2023) and of 70 journal and conference pape
rs on control theory and applied mathematics. \nA. Mironchenko serves as a
n Associate Editor in Systems & Control Letters and is a co-founder and co
-organizer of the biennial Workshop series “Stability and Control of Inf
inite-Dimensional Systems” (SCINDIS\, 2016 - now). He is a Senior Member
of IEEE.\nHe is a recipient of 2023 IEEE CSS George S. Axelby Outstanding
Paper Award.\n\nHis research interests include stability theory\, nonline
ar systems theory\, distributed parameter systems\, hybrid systems\, and a
pplications of control theory to biological systems and distributed contro
l.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Andrieu (LAGEPP\, University of Lyon\, France)
DTSTART;VALUE=DATE-TIME:20240515T150000Z
DTEND;VALUE=DATE-TIME:20240515T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/43
DESCRIPTION:by Vincent Andrieu (LAGEPP\, University of Lyon\, France) as p
art of Input-to-State Stability and its Applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pauline Bernard (Mines Paris\, France)
DTSTART;VALUE=DATE-TIME:20240522T150000Z
DTEND;VALUE=DATE-TIME:20240522T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/44
DESCRIPTION:by Pauline Bernard (Mines Paris\, France) as part of Input-to-
State Stability and its Applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tengfei Liu (Northeastern University\, China)
DTSTART;VALUE=DATE-TIME:20240529T150000Z
DTEND;VALUE=DATE-TIME:20240529T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/45
DESCRIPTION:Title: Singular Perturbation: When the Perturbation Parameter Becomes a State
-Dependent Function\nby Tengfei Liu (Northeastern University\, China)
as part of Input-to-State Stability and its Applications\n\n\nAbstract\nTh
is paper introduces a new class of singularly perturbed systems in which t
he small\, but constant\, perturbation coefficient in standard singular pe
rturbation theory is replaced by a state-dependent function. This generali
zation is aimed at broadening the applicability of singular perturbation t
heory in practice. For this class of singularly perturbed systems\, it is
assumed that the boundary-layer subsystem is globally asymptotically stabl
e (GAS) at the origin and the reduced subsystem is input-to-state stable (
ISS) with respect to the state of the boundary-layer subsystem. Under a mi
ld monotonicity condition\, sufficient conditions on the perturbation func
tions are given under which the singularly perturbed system is GAS at the
origin. ISS and nonlinear small-gain techniques are exploited in the stabi
lity analysis. The efficacy of the proposed theoretical result is validate
d via its applications to tackling integral control and feedback optimizat
ion problems.\n\n**Biography** Tengfei Liu received the B.E. degree in
automation\, in 2005\, the M.E. degree in control theory and control engin
eering\, in 2007\, both from South China University of Technology\, and th
e Ph.D. degree in engineering from RSISE\, the Australian National Univers
ity\, Canberra\, in 2011. From 2011 to 2013\, he was a Postdoc with facult
y fellowship at Polytechnic Institute of New York University. Since 2014\,
he has been associated with the State Key Laboratory of Synthetical Autom
ation for Process Industries at Northeastern University\, China\, where he
holds the position of full professor. His research interests include stab
ility and control of interconnected nonlinear systems. He has served as As
sociate Editor for IEEE Transactions on Automatic Control\, Systems and Co
ntrol Letters\, and Science China: Information Sciences. Dr. Liu is a seni
or member of IEEE.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Girard (L2S Paris-Saclay\, France)
DTSTART;VALUE=DATE-TIME:20240612T150000Z
DTEND;VALUE=DATE-TIME:20240612T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/46
DESCRIPTION:by Antoine Girard (L2S Paris-Saclay\, France) as part of Input
-to-State Stability and its Applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Bisoffi (Politecnico di Milano\, Italy)
DTSTART;VALUE=DATE-TIME:20240703T150000Z
DTEND;VALUE=DATE-TIME:20240703T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112728Z
UID:ISS-Theory/47
DESCRIPTION:by Andrea Bisoffi (Politecnico di Milano\, Italy) as part of I
nput-to-State Stability and its Applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/47/
END:VEVENT
END:VCALENDAR