Low-Gain Compensation for PDE-ODE Cascade Systems With Distributed Diffusion and Counter Convection

• 成果类型: Article
• 署名作者: Xu, Xiang; Liu, Lu; Krstic, Miroslav; Feng, Gang
• 署名单位: City University of Hong Kong; 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.2022.3170371
• 发表日期: 2023
• 页码: 2360-2367
• 关键词: Counter convection; distributed diffusion; low-gain compensation; PDE-ODE cascade system

摘要

This article proposes two low-gain controllers for systems with distributed input dynamics, governed by diffusion equations with counter convection. It is shown that the considered PDE-ODE cascade system can be exponentially stabilized with the proposed low-gain controllers as long as the open-loop plant is not exponentially unstable. A key advantage of the proposed controllers is their much simplified form in comparison with the existing backstepping-designed controllers developed for the same systems. However at the same time, additional restrictions on the eigenvalues of the open-loop plant have to be imposed for low-gain controllers, which are not required in the backstepping design. Moreover, the Robin boundary condition, which is more general and also more difficult to deal with, is considered in this article. Several simulation examples are provided to illustrate effectiveness of our controllers.