Data-Driven Inference on Optimal Input-Output Properties of Polynomial Systems With Focus on Nonlinearity Measures

• 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.2022.3226652
• 发表日期: 2023
• 页码: 2832-2847
• 关键词: trajectory; Linear approximation; estimation; Time-domain analysis; optimization; Noise measurement; Linear systems; Data-driven system analysis; identification for control; polynomial dynamical systems

摘要

In the context of dynamical systems, nonlinearity measures quantify the strength of nonlinearity by means of the distance of their input-output behavior to a set of linear input-output mappings. In this article, we establish a framework to determine nonlinearity measures and other optimal input-output properties for nonlinear polynomial systems without explicitly identifying a model but from a finite number of input-state measurements, which are subject to noise. To this end, we deduce from data for the unidentified ground-truth system three possible set-membership representations, compare their accuracy, and prove that they are asymptotically consistent with respect to the amount of samples. Moreover, we leverage these representations to compute guaranteed upper bounds on nonlinearity measures and the corresponding optimal linear approximation model via semidefinite programming. Furthermore, we extend the established framework to determine optimal input-output properties described by time domain hard integral quadratic constraints.