Regulation-triggered adaptive control of a hyperbolic PDE-ODE model with boundary interconnections

We present a certainty equivalence-based adaptive boundary control scheme with a regulation-triggered batch least-squares identifier, for a heterodirectional transport partial differential equation-ordinary differential equation (PDE-ODE) system where the transport speeds of both transport PDEs are unknown. We use a nominal controller which is fed piecewise-constant parameter estimates from an event-triggered parameter update law that applies a least-squares estimator to data “batches” collected over time intervals between the triggers. A parameter update is triggered by an observed growth in the norm of the PDE state. The proposed triggering-based adaptive control guarantees: (1) the absence of a Zeno phenomenon; (2) parameter estimates are convergent to the true values in finite time (from most initial conditions); (3) exponential regulation of the plant states to zero. The effectiveness of the proposed design is verified by a numerical example.