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

Ji Wang; Miroslav Krstic

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arXiv · 2110.05680

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

Ji Wang·Miroslav Krstic

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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.

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BibTeX RIS

Ji Wang, Miroslav Krstic. 2021-10-12. Event-Triggered Adaptive Control of a Parabolic PDE-ODE Cascade with Piecewise-Constant Inputs and Identification. https://arxiv.org/abs/2110.05680

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