Stability Verification of Neural Network Controllers Using Mixed-Integer Programming

• 成果类型: Article
• 署名作者: Schwan, Roland; Jones, Colin N.; Kuhn, Daniel
• 署名单位: Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; 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.2023.3283213
• 发表日期: 2023
• 页码: 7514-7529
• 关键词: mixed-integer programming; model predictive control; Neural Networks; stability guarantees; verification

摘要

In this article, we propose a framework for the stability verification of mixed-integer linear programming (MILP) representable control policies. This framework compares a fixed candidate policy, which admits an efficient parameterization and can be evaluated at a low computational cost, against a fixed baseline policy, which is known to be stable but expensive to evaluate. We provide sufficient conditions for the closed-loop stability of the candidate policy in terms of the worst-case approximation error with respect to the baseline policy, and we show that these conditions can be checked by solving a mixed-integer quadratic program. In addition, we demonstrate that an outer and inner approximation of the stability region of the candidate policy can be computed by solving an MILP. The proposed framework is sufficiently general to accommodate a broad range of candidate policies including ReLU neural networks (NNs), optimal solution maps of parametric quadratic programs, and model predictive control (MPC) policies. We also present an open-source toolbox in Python based on the proposed framework, which allows for the easy verification of custom NN architectures and MPC formulations. We showcase the flexibility and reliability of our framework in the context of a dc-dc power converter case study and investigate its computational complexity.