NULL CONTROL OF CHAFEE-INFANTE EQUATIONS WITH SPATIALLY SCHEDULED ACTUATORS AND SENSORS

This paper addresses a switched sampled-data control design for stabilization of Chafee-Infante reaction-diffusion equation under Dirichlet boundary conditions with spatially scheduled actuators. The interval $[0, L]$ is divided into $N$ subdomains. It is assumed that discrete-time point-like or average measurements are available and $N$ sensors are placed in each subdomain and measure the average value of the state in the discrete time. The system is stabilized by switching sampled-data static output-feedback. A suitable control law for switching sampled-data is given. The proposed switching controller can be implemented either by placing $N$ actuators and sensors in each subdomain or by using an actuator-sensor pair that can move to the active subdomain. Constructive conditions are derived to ensure that the resulting closed-loop system is exponentially stable by means of the Lyapunov approach. Numerical example verifies our results.