Local Stabilization of an Unstable Parabolic Equation via Saturated Controls

• 成果类型: Article
• 署名作者: Mironchenko, Andrii; Prieur, Christophe; Wirth, Fabian
• 署名单位: University of Passau; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3007733
• 发表日期: 2021
• 页码: 2162-2176
• 关键词: Mathematical model; Eigenvalues and eigenfunctions; Heating systems; DELAYS; Lyapunov methods; Closed loop systems; Attraction region; partial differential equation (PDE) control; reaction-diffusion equation; saturated control; stabilization

摘要

We derive a saturated feedback control, which locally stabilizes a linear reaction-diffusion equation. In contrast to most other works on this topic, we do not assume the Lyapunov stability of the uncontrolled system and consider general unstable systems. Using Lyapunov methods, we provide estimates for the region of attraction for the closed-loop system, given in terms of linear and bilinear matrix inequalities. We show that our results can be used with distributed as well as scalar boundary control, and with different types of saturations. The efficiency of the proposed method is demonstrated by means of numerical simulations.