Reduced-Order Nonlinear Observers Via Contraction Analysis and Convex Optimization

• 成果类型: Article
• 署名作者: Yi, Bowen; Wang, Ruigang; Manchester, Ian R.
• 署名单位: University of Sydney; University of Sydney
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3115887
• 发表日期: 2022
• 页码: 4045-4060
• 关键词: Observers; Convex functions; CONVERGENCE; tools; Task analysis; Symmetric matrices; STANDARDS; Contraction analysis; Convex Optimization; nonlinear system; state observer

摘要

In this article, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization. Despite the fact that contraction is a concept naturally suitable for state estimation, the existing solutions are either local or relatively conservative when applying to physical systems. To address this, we show that this problem can be translated into an offline search for a coordinate transformation after which the dynamics is (transversely) contracting. The obtained sufficient condition consists of some easily verifiable differential inequalities, which, on one hand, identify a very general class of detectable nonlinear systems, and on the other hand, can be expressed as computationally efficient convex optimization, making the design procedure more systematic. Connections with some well-established approaches and concepts are also clarified in this article. Finally, we illustrate the proposed method with several numerical and physical examples, including polynomial, mechanical, electromechanical, and biochemical systems.