Near-Optimal Control for Nonzero-Sum Differential Games of Continuous-Time Nonlinear Systems Using Single-Network ADP

TLDR: The novel weight tuning laws for critic neural networks are proposed, which not only ensure the Nash equilibrium to be reached but also guarantee the system to be stable and demonstrate the uniform ultimate boundedness of the closed-loop system.

Abstract: In this paper, a near-optimal control scheme is proposed to solve the nonzero-sum differential games of continuous-time nonlinear systems. The single-network adaptive dynamic programming (ADP) is utilized to obtain the optimal control policies which make the cost functions reach the Nash equilibrium of nonzero-sum differential games, where only one critic network is used for each player instead of the action-critic dual network used in a typical ADP architecture. Furthermore, the novel weight tuning laws for critic neural networks are proposed, which not only ensure the Nash equilibrium to be reached but also guarantee the system to be stable. No initial stabilizing control policy is required for each player. Moreover, Lyapunov theory is utilized to demonstrate the uniform ultimate boundedness of the closed-loop system. Finally, a simulation example is given to verify the effectiveness of the proposed near-optimal control scheme.