Event-Triggered Control of PDE Systems
摘要
Chapter 3 presented time-triggered sampled-data control of PDEs via the time-delay approach to the corresponding Lyapunov functionals. In this chapter we consider event-triggered control for 1D nonlinear KdV equation, where the time-delay approach does not work (it seems to be impossible to construct an appropriate Lyapunov functionals because of the third spatial derivative in KdV equation). In this chapter, we introduce an innovative event-triggering mechanism to the sampled control law, aiming at optimizing control input updates by restricting them to meaningful instants. This approach not only alleviates computational burdens but also bolsters system efficiency. This approach also addresses the challenges of maintaining system stability and avoiding Zeno behavior. We establish sufficient conditions based on LMIs to guarantee regional exponential stability of the closed-loop system.