Adaptive event-triggered PDE control for load-moving cable systems

Motivated by lateral vibration suppression of a mining cable elevator, which is load-moving system, where the load moves along viscoelastic guideway whose stiffness and damping coefficients are unknown, we present event-triggered adaptive output-feedback boundary control design hyperbolic PDE–ODE coupled system using measurements at PDE actuated ODE, subsystem class 2 × PDEs with spatially-varying on time-varying domain, high uncertainty exist in matrix ODE uncontrolled PDE. A continuous-in-time observer-based backstepping law designed gains can be self-tuned to adjust into given target matrix, based an dynamic event-triggering mechanism built existence minimal dwell-time proved. The asymptotic stability overall event-based closed-loop proved via Lyapunov analysis. In numerical simulation, performance proposed controller verified elevator.