Robustly Learning Regions of Attraction From Fixed Data

• 成果类型: Article
• 署名作者: Tacchi, Matteo; Lian, Yingzhao; Jones, Colin N.
• 署名单位: Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Huawei Technologies; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3462528
• 发表日期: 2025
• 页码: 1576-1591
• 关键词: Lyapunov methods; POLYNOMIALS; computational modeling; Numerical stability; mathematical models; trajectory; Thermal stability; Machine Learning; optimization; Robust control; stability of nonlinear systems; uncertain systems

摘要

While stability analysis is a mainstay for control science, especially computing regions of attraction of equilibrium points, until recently most stability analysis tools always required explicit knowledge of the model or a high-fidelity simulator representing the system at hand. In this work, a new data-driven Lyapunov analysis framework is proposed. Without using the model or its simulator, the proposed approach can learn a piecewise affine Lyapunov function with a finite and fixed offline dataset. The learnt Lyapunov function is robust to any dynamics that are consistent with the ofline dataset, and its computation is based on second-order cone programming. Along with the development of the proposed scheme, a slight generalization of the classical Lyapunov stability criteria is derived, enabling an iterative inference algorithm to augment the region of attraction.