Event-Triggered Control for Stabilization of Semilinear N-D Reaction-Convection-Diffusion PDE by Switching

Abstract

This paper addresses a switched sampled-data control design for stabilization of the N-dimensional (N-D) semilinear heat equation with a mobile actuator. It is supposed that discrete-time averaged measurements are available. The system is known to be stabilizable by the static output-feedback employing several distributed in space actuators and sensors, but is not stabilizable by only one of the actuator-sensor pairs. Does there exist a switching stabilizing static output-feedback such that at all times, only one actuator-sensor pair is active? In our recent paper we gave a positive answer and found the appropriate switching sampled-data time-triggered control law for the one-dimensional (1-D) case. In this paper, to enlarge the time between switching (which means to reduce the frequency of actuator moving to the active domain), we present an event-triggered control for stabilization by switching. Moreover, we extend the results for stabilization by switching to the N-D case. Numerical examples show that the switching-based event-triggered controller essentially decreases the frequency of the actuator moving compared to the time-triggered controller, reducing operating costs.