Adaptive robust control without initial stabilizing for constrained-states nonlinear multiplayer mixed zero-sum game systems with matched input disturbances

In this paper, for the multiplayer mixed zero-sum game (MZSG) problem of the constrained-states nonlinear systems with matched input disturbances, an adaptive robust control method without initial stabilizing is presented on account of barrier function (BF) transformation. Firstly, the original system with state constraints is converted to a transformed system without state constraints by barrier function transformation. Secondly, to overcome the influence of matched input disturbances, considering the nominal system related to the transformation system, the cost function corresponding to each player is appropriately selected, and the robust regulation scheme with matched input disturbances is converted to the optimal regulation scheme. In addition, a novel weight tuning law is designed for the critic neural network (NN) by combining the experience replay (ER) mechanism and the index function. Then, the corresponding cost function of each player is approximated by the critic NN without requiring initial stabilizing control. Utilizing the Lyapunov stability theory, under the influence of state constraints and matched input disturbances, the critic NN weights and states within the multiplayer system are ensured to be uniformly ultimately bounded (UUB). Ultimately, the validity of the proposed method is verified by two simulation examples.