Reliably-Stabilizing Piecewise-Affine Neural Network Controllers

• 成果类型: Article
• 署名作者: Fabiani, Filippo; Goulart, Paul J.
• 署名单位: University of Oxford; IMT School for Advanced Studies Lucca
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3216978
• 发表日期: 2023
• 页码: 5201-5215
• 关键词: Mixed-integer (MI) linear optimization; model predictive control (MPC); neural networks (NNs)

摘要

A common problem affecting neural network (NN) approximations of model predictive control (MPC) policies is the lack of analytical tools to assess the stability of the closed-loop system under the action of the NN-based controller. We present a general procedure to quantify the performance of such a controller, or to design minimum complexity NNs with rectified linear units (ReLUs) that preserve the desirable properties of a given MPC scheme. By quantifying the approximation error between NN-based and MPC-based state-to-input mappings, we first establish suitable conditions involving two key quantities, the worst-case error and the Lipschitz constant, guaranteeing the stability of the closed-loop system. We then develop an offline, mixed-integer optimization-based method to compute those quantities exactly. Together these techniques provide conditions sufficient to certify the stability and performance of an ReLU-based approximation of an MPC control law.