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Pré-Publication, Document De Travail Année : 2023

Event-triggered boundary control of an unstable reaction diffusion PDE with input delay

Résumé

In chemical, biological, or population (epidemiological) processes the feedback action may be considerably delayed by time-consuming chemical measurements or biological tests. With such large delays on the control action in mind, and motivated by the fact that in some of these systems only piecewise-constant inputs can be applied between time instants at which measurements trigger changes in control, we consider the problem of event-triggered stabilization of 1-D reaction-diffusion PDE systems with input delay. The approach relies on reformulating the delay problem as an actuated transport PDE which cascades into the reaction-diffusion PDE, and on the emulation of backstepping control. The paper proposes a static (state-dependent) triggering condition which establishes the time instants at which the control value needs to be updated. It is shown that under the proposed event-triggered boundary control, there exists a minimal dwelltime (independent of the initial conditions) between two triggering times which allows to guarantee the well-posedness of the closed-loop system, and the exponential stability. The stability analysis is based on Input-to-State stability theory for PDEs and small-gain arguments. A simulation example is presented to validate the theoretical results.
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Dates et versions

hal-04304378 , version 1 (24-11-2023)

Identifiants

  • HAL Id : hal-04304378 , version 1

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Florent Koudohode, Nicolás Espitia, Miroslav Krstic. Event-triggered boundary control of an unstable reaction diffusion PDE with input delay. 2023. ⟨hal-04304378⟩
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