Event-Triggered Adaptive Control of a Parabolic PDE-ODE Cascade With Piecewise-Constant Inputs and Identification

We present an adaptive event-triggered boundary control scheme for a parabolic PDE-ODE system, where the reaction coefficient of PDE, and system parameter scalar ODE, are unknown. In proposed controller, estimates, which built by batch least-square identification, recomputed plant states resampled simultaneously. As result, both estimates input employ piecewise-constant values. closed-loop following results proved: 1) absence Zeno phenomenon; 2) finite-time exact identification unknown parameters under most initial conditions (all except set measure zero); 3) exponential regulation to zero. A simulation example is presented validate theoretical result.