Event-Triggered Control Through the Eyes of Hybrid Small-Gain Theorem

Abstract: A common approach to design event-triggered controllers is emulation. The idea is to first construct a feedback law in continuous-time, which ensures the desired closed-loop properties. Then, the communication constraints between the plant and the controller are taken into account and a triggering rule is 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 in practice.

Various triggering rules have been proposed in this context in the literature, including relative threshold, fixed threshold, dynamic 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 conditions of a hybrid small-gain theorem. This unifying perspective provides clear viewpoints on the essential differences and similarities of existing event-triggering policies. Interestingly, for all the considered laws, the small-gain condition vacuously holds in the sense that one of the interconnection 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 trivially satisfied. By doing so, we obtain redesigned strategies, which may reduce the number of transmissions as illustrated by an example.

systems and controlanalysis of PDEsclassical analysis and ODEsdynamical systemsoptimization and control

Audience: researchers in the topic

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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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