Construction of Continuous and Piecewise Affine Feedback Stabilizers for Nonlinear Systems

• 成果类型: Article
• 署名作者: Steentjes, Tom Robert Vince; Lazar, Mircea; Doban, Alina Ionela
• 署名单位: Eindhoven University of Technology; Eindhoven University of Technology; ASML Holding
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3030864
• 发表日期: 2021
• 页码: 4059-4068
• 关键词: Lyapunov methods; Nonlinear systems; Stability criteria; Closed loop systems; interpolation; computational methods; Lyapunov methods; stability of nonlinear systems; stabilization

摘要

In this article, two methods for constructing continuous and piecewise affine (CPA) feedback stabilizers for nonlinear systems are presented. First, a construction based on a piecewise affine interpolation of Sontag's universal formula is developed. Stability of the corresponding closed-loop system is verified a posteriori by means of a CPA control Lyapunov function and subsequently solving a feasibility problem. Second, we develop a procedure for computing CPA feedback stabilizers via linear programming, which allows for the optimization of a control-oriented criterion in the synthesis procedure. Stability conditions are a priori specified in the linear program, which removes the necessity for a posteriori verification of closed-loop stability. We illustrate the developed methods via two application-inspired examples considering the stabilization of an inverted pendulum and the stabilization of a healthy equilibrium of the hypothalamic-pituitary-adrenal axis.