Event-Triggered Adaptive Control of Coupled Hyperbolic PDEs With Piecewise-Constant Inputs and Identification

In this article, we present an event-triggered boundary control scheme with a, likewise, event-triggered batch least-squares parameter identification for a $2\times 2$ hyperbolic PDE-ODE system, where two coefficients of the in-domain couplings between two transport PDEs, and the system parameter of a scalar ODE, are unknown. The triggering condition is designed based on evaluating both the actuation deviation caused by the difference between the plant states and their sampled values, and the growth of the plant norm. When either condition is met, the piecewise-constant control input and parameter estimates are updated simultaneously. For the closed-loop system, the following results are proved: first, the absence of a Zeno phenomenon; second, finite-time exact identification of the unknown parameters in most situations; third, exponential regulation of the plant states to zero. In the numerical simulation, the design is verified in an application of axial vibration control of a mining cable elevator, where the damping coefficients of the cable and the cage are unknown.