Reinforcement learning and neural networks for multi-agent nonzero-sum games of nonlinear constrained-input systems

This paper presents an online adaptive optimal control method based on reinforcement learning to solve the multi-agent nonzero-sum (NZS) differential games of nonlinear constrained-input continuous-time systems. A non-quadratic cost functional associated with each agent is employed to encode the saturation nonlinearity into the NZS game. The algorithm is implemented as a separate actor-critic neural network (NN) structure for every participant in the game, where adaptation of both NNs is performed simultaneously and continuously. The technique of concurrent learning is utilized to obtain novel update laws for the critic NN weights. That is, recorded data and current data are used concurrently for adaptation of the critic NN weights. This results in an algorithm where an easier and verifiable condition is sufficient for parameter convergence rather than the restrictive persistence of excitation (PE) condition. The stability of the closed-loop systems is guaranteed and the convergence to the Nash equilibrium solution of the game is shown. Simulation results show the effectiveness of the proposed method.