Event-Triggered Output-Feedback Backstepping Control of Sandwich Hyperbolic PDE Systems

Abstract

Motivated by vibration control of a mining cable elevator avoiding frequent actions of a massive actuator, which is a hydraulic cylinder driving a head sheave, we present an event-triggered output-feedback backstepping boundary controller for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2\times 2$</tex-math></inline-formula> coupled hyperbolic partial differential equations (PDEs) sandwiched by two ordinary differential equations (ODEs), through a two-step design including an output-feedback low-pass-filter-based backstepping boundary stabilization law and the subsequent design of a dynamic event-triggering mechanism. The existence of a minimal dwell-time between two triggering times, and exponential convergence in the event-based closed-loop system are proved in this article. In numerical simulations, the proposed control design is validated in the application of axial vibration control of a mining cable elevator.