Backstepping Control of Coupled General Hyperbolic-Parabolic PDE-PDE Systems

• 成果类型: Article
• 署名作者: Deutscher, Joachim; Gehring, Nicole; Jung, Nick
• 署名单位: Ulm University; Johannes Kepler University Linz
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3340119
• 发表日期: 2024
• 页码: 3465-3472
• 关键词: Backstepping; coupled hyperbolic-parabolic systems; observer design; state feedback design

摘要

This article considers the backstepping state feedback and observer design for hyperbolic and parabolic PDEs, which are bidirectionally interconnected in a general coupling structure. Both PDE subsystems consist of coupled scalar PDEs with the heterodirectional hyperbolic PDE subsystem subject to actuation and sensing. By making use of a multistep approach to construct the transformation into a stable target system, it is shown that a backstepping state feedback and observer design only requires to solve the well-known kernel equations for the hyperbolic and parabolic subsystems as well as additional decoupling equations. The latter are standard initial boundary value problems for parabolic PDEs. This significantly facilitates the well-posedness analysis and the numerical computation of the backstepping controller. Exponential stability is verified for the state feedback loop, the observer error dynamics, and the closed-loop system using an observer-based compensator. The proposed backstepping design procedures are demonstrated for numerical examples.