Robust control design for multi-player nonlinear systems with input disturbances via adaptive dynamic programming

Abstract

In this paper, a novel robust control strategy based on adaptive dynamics programming (ADP) technique is proposed for multi-player nonlinear systems with input disturbances. A pair of robust control policies is constructed by multiplying appropriate coupling gains to the Nash solution of nominal nonlinear nonzero-sum game with predefined cost functions accounting for system uncertain disturbances. Sufficient conditions for the existence of robust control strategy are derived, and it is proved that the robust control strategy can guarantee the multi-player nonlinear systems to be stable in the sense of uniform ultimate boundedness (UUB) with disturbance rejection. The single-network ADP algorithm is employed to solve the coupled Hamilton–Jacobi equations, where only requires to online tune the weights of critic neural networks (NN) for each player. By utilizing Lyapunov theory, the NN weight estimation errors are proved to be uniformly ultimately bounded, while the stability of the closed-loop nonzero-sum game system is also guaranteed. Two numerical experiments are given to demonstrate the effectiveness of the proposed approach.