Non-zero sum Nash Q-learning for unknown deterministic continuous-time linear systems

This work proposes a novel Q-learning algorithm to solve the problem of non-zero sum Nash games of linear time invariant systems with NN-players (control inputs) and centralized uncertain/unknown dynamics. We first formulate the Q-function of each player as a parametrization of the state and all other the control inputs or players. An integral reinforcement learning approach is used to develop a model-free structure of NN-actors/NN-critics to estimate the parameters of the NN-coupled Q-functions online while also guaranteeing closed-loop stability and convergence of the control policies to a Nash equilibrium. A 4th order, simulation example with five players is presented to show the efficacy of the proposed approach.