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.