Análise de estabilidade de sistemas lineares controlados por redes neurais emulando MPC

Daniel Vargas Zanette; Leonardo Cabral; João Manoel Gomes da Silva Jr.; Giorgio Valmorbida

doi:10.20906/SBAI-SBSE-2023/3868

Daniel Vargas Zanette Programa de Pós-graduação em Engenharia Elétrica, Universidade Federal do Rio Grande do Sul, RS
Leonardo Cabral Programa de Pós-graduação em Engenharia Elétrica, Universidade Federal do Rio Grande do Sul, RS
João Manoel Gomes da Silva Jr. Programa de Pós-graduação em Engenharia Elétrica, Universidade Federal do Rio Grande do Sul, RS
Giorgio Valmorbida Laboratoire des Signaux et Systèmes, CentraleSupèlec, CNRS, Université Paris-Saclay

DOI: https://doi.org/10.20906/SBAI-SBSE-2023/3868

Keywords: Neural Network, Model Predictive Control, Lyapunov methods

Abstract

This work studies the problem of exponential stability analysis of the origin of a discrete-time linear system controlled by a ReLU-type Neural Network (NN) that approximates a Model Predictive Control (MPC). Firstly, it is shown that the closed-loop system is equivalent to a Piecewise Affine (PWA) system that can be described by an implicit representation based on ramp functions. Using this representation, conditions in the form of LMIs for the stability certification of the origin of the closed-loop system operated with NN control are derived. In addition, the amplitude constraints on the control signal are taken into account in the stability analysis in the form of a (potentially asymmetric) saturation in the NN output. Finally, a numerical example demonstrates the application of the proposed conditions.