Parallel Control for Nonzero-Sum Games With Completely Unknown Nonlinear Dynamics via Reinforcement Learning

This article utilizes parallel control to investigate the problem of continuous-time (CT) nonzero-sum games (NZSGs) for completely unknown nonlinear systems via reinforcement learning (RL), and a parallel control-based NZSG (PNZSG) method is developed without reconstructing unknown dynamics or employing off-policy integral RL (IRL). First, novel dynamic control policies (DCPs) are developed for NZSGs by introducing controls into feedback, and an augmented system with augmented performance indices is constructed to derive the DCPs. Then, we theoretically analyze the effect of the DCPs on the control stability and performance indices, and the optimality of PNZSG is proven to be equivalent to the optimality of the original NZSGs. Subsequently, an IRL technique is employed to achieve the developed PNZSG method, and we show that no prior knowledge of the dynamics of NZSGs is needed to deploy the developed PNZSG method because of the augmented system and performance indices. Finally, numerical examples, including cooperative adaptive cruise control (CACC) of a vehicular platoon, demonstrate the correctness of the developed PNZSG method. The associated code is available at: <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/lujingweihh/Adaptive-dynamic-programming-algorithms/tree/main/model_free_nonzero_sum_games</uri>.