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

受到侧向振动的激励抑制采矿电缆升降机（这是一种载荷移动电缆系统），其中载荷沿着刚度和阻尼系数未知的粘弹性导轨运动，我们提出了双曲线PDE-ODE的事件触发式自适应输出-反馈边界控制设计耦合系统，使用PDE激励边界和ODE进行测量，其中PDE子系统是一类2×2耦合双曲PDE，具有空间变化系数和时变域，并且系统矩阵中存在很高的不确定性在PDE不受控制的边界处的ODE子系统的位置。设计了一种基于连续观察者的自适应反推控制律，其中可以对控制增益进行自调整，以将ODE的系统矩阵调整为给定的目标系统矩阵，在此基础上，建立了基于观察者的动态事件触发机制，并证明了最小停留时间的存在。这通过Lyapunov分析证明了基于事件的自适应输出反馈闭环系统整体的渐近稳定性。在数值模拟中，所提出的控制器的性能在采矿缆索电梯的横向振动抑制中得到了验证。