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

• 成果类型: Article
• 署名作者: Wang, Ji; Krstic, Miroslav
• 署名单位: Xiamen University; University of California System; University of California San Diego
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3227916
• 发表日期: 2023
• 页码: 5493-5508
• 关键词: adaptive control; Backstepping; event-triggered control; least-squares identifier; parabolic PDEs

摘要

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.