Jorge Cortés

Professor

Cymer Corporation Endowed Chair





Performance-barrier-based event-triggered boundary control of a class of reaction-diffusion PDEs
B. Rathnayake, M. Diagne, J. Cortés, M. Krstic
Automatica, submitted


Abstract

We employ the recent performance-barrier-based event-triggered control (P-ETC) for stabilization of a class of reaction-diffusion PDEs with Dirichlet boundary actuation. Rather than insisting on a strictly monotonic decrease of the Lyapunov function for the closed-loop system, P-ETC allows the Lyapunov function to increase as long as it remains below an acceptable performance barrier. This approach integrates a performance residual-the difference between the value of the performance barrier and the Lyapunov function-into the triggering mechanism. The integration adds flexibility and results in fewer control updates than with strategies that demand a monotonic decrease of the Lyapunov function. Our P-ETC PDE backstepping designs ensure global exponential convergence in the spatial L2 norm, without encountering the Zeno phenomenon. To avoid continuous monitoring of the triggering function, we develop periodic event-triggered and self-triggered variants (P-PETC and P-STC, respectively) of P-ETC. P-PETC only requires periodic evaluation whereas the P-STC preemptively computes the time of the next event at the current event time using the system model and the continuously available system states. P-PETC and P-STC also ensure a Zeno-free behavior and deliver performance equivalent to that of continuous-time P-PETC, which requires a continuous computation of the triggering function, in addition to the continuous sensing of the state. We provide numerical simulations to demonstrate the effectiveness of our technique against the regular event-triggered boundary control design, the latter being associated with strictly decreasing Lyapunov functions.

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Mechanical and Aerospace Engineering, University of California, San Diego
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