Adaptive Regulation- Triggered Control of Hyperbolic PDEs by Batch Least-Squares

In this paper, we present an adaptive boundary control scheme with a regulation-triggered batch least-squares identifier, for a heterodirectional transport PDE-ODE system where the transport speeds of both transport PDEs are unknown. The proposed scheme includes a certainty-equivalence controller and a least-squares identifier updated at a sequence of time instants, which is determined by an event trigger designed based on the progress of regulation of the plant states. The proposed adaptive regulation-triggered control guarantees: 1) The absence of a Zeno behavior; 2) Exact estimation of the transport speeds in only one trigger for non-zero initial conditions; 3) Exponential regulation of the plant states to zero. The effectiveness is verified by a numerical example.