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

TL;DR

This paper introduces an adaptive event-triggered boundary control method for a parabolic PDE-ODE system with unknown parameters, ensuring finite-time parameter identification and exponential state regulation without Zeno behavior.

Contribution

It develops a novel control scheme combining batch least-square identification with event-triggered updates for PDE-ODE systems with piecewise-constant inputs.

Findings

No Zeno phenomenon occurs in the closed-loop system.

Finite-time exact identification of unknown parameters is achieved.

Plant states are exponentially stabilized to zero.

Abstract

We present an adaptive event-triggered boundary control scheme for a parabolic 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); 3) exponential regulation of the plant states to zero. A simulation example is presented to validate the theoretical result.