Data-Driven System Analysis of Nonlinear Systems Using Polynomial Approximation

• 成果类型: Article
• 署名作者: Martin, Tim; Allgoewer, Frank
• 署名单位: University of Stuttgart
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3321212
• 发表日期: 2024
• 页码: 4261-4274
• 关键词: Noise measurement; system dynamics; nonlinear dynamical systems; trajectory; Linear matrix inequalities; control theory; Upper bound; Data-driven system analysis; Dissipativity; Nonlinear systems; Polynomial Approximation

摘要

In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we establish a polynomial representation of nonlinear functions based on a polynomial sector by Taylor's theorem and a set-membership for Taylor polynomials. The latter is obtained from finite noisy samples. By incorporating the measurement noise, the error of polynomial approximation, and potentially given prior knowledge on the structure of the system dynamics, we achieve computationally tractable conditions by sum of squares relaxation to verify dissipativity of nonlinear dynamical systems with rigorous guarantees. The framework is extended by combining multiple Taylor polynomial approximations, which yields a less conservative piecewise polynomial system representation. The proposed approach is applied for an experimental example. There it is compared with a least-squares-error model including knowledge from first principle.