Fixed-Time ISS and Prescribed-Time Stabilization

Miroslav Krstic (UC San Diego, USA)

22-Jul-2021, 15:00-16:00 (3 years ago)

Abstract: In prescribed-time stabilization the task is to design a feedback law that guarantees completion of the convergence to a set point 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 perfectly and the full state is measured, ISS issues do not arise. However, in the presence of disturbances or under observer-based feedback, ISS with respect 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 origin, which is not necessarily the system’s equilibrium, is made attractive 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 to 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 PDEs (in hyperbolic PDEs, finite-time stabilization, when possible, is obtained as easily as exponential stabilization).

systems and controlanalysis of PDEsclassical analysis and ODEsdynamical systemsoptimization and control

Audience: researchers in the topic


Input-to-State Stability and its Applications

Series comments: This is a seminar for the exchange of ideas in input-to-state stability (ISS) theory and related fields.

The scope of the Seminar includes but is not limited to

- ISS for finite-dimensional systems (ODEs, hybrid, impulsive, switched, discrete-time systems),

- Infinite-dimensional ISS theory (PDEs, evolution equations in Banach spaces, time-delay systems, infinite networks)

- Applications to robust control and observation, nonlinear control, network analysis, etc.

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Organizers: Andrii Mironchenko*, Patrick Bachmann*
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