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