Event-triggered Backstepping Control of 2 × 2 Hyperbolic PDE-ODE Systems

Abstract Motivated by vibration control of a mining cable elevator avoiding frequent actions of the actuator which is a massive hydraulic cylinder at the head sheave, we present an event-triggered backstepping boundary controller for a 2 x 2 coupled hyperbolic PDE-ODE system. A two-step design is proposed including the design of a low-pass-filter-based backstepping boundary stabilization law and the sequent design of an event-trigger mechanism. The proof of the existence of a nonzero minimal dwell-time between two triggering times, and the exponential stability result of the event-based closed-loop system are given in this paper.