Local Output Feedback Stabilization of a Nonlinear Kuramoto-Sivashinsky Equation

• 成果类型: Article
• 署名作者: Lhachemi, Hugo
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3293722
• 发表日期: 2023
• 页码: 8165-8170
• 关键词: Finite-dimensional control; Kuramoto-Sivashinsky partial differential equation (PDE); multi-input-multi-output (MIMO); output feedback stabilization

摘要

This article is concerned with the local output feedback stabilization of a nonlinear Kuramoto-Sivashinsky equation. The control is located at the boundary of the domain while the measurement is selected as a Neumann trace. This choice of system output requires the study of the system trajectories in H-2-norm. Moreover, the choice of the actuation/sensing scheme is discussed and adapted depending on the parameters of the plant in order to avoid the possible loss of controllability/observability property of certain eigenvalues of the underlying operator. This leads in certain cases to a multi-input-multi-output control design procedure. The adopted control strategy is finite dimensional and relies on spectral reduction methods. We derive sufficient conditions ensuring the local exponential stabilization of the plant. These control design constraints are shown to be feasible, provided the order of the controller is selected to be large enough, ensuring that the reported control design procedure is systematic.