Adaptive MPC for multi-player systems with parametric uncertainties: The noncooperative game case

In this paper, the distributed adaptive model predictive noncooperative game problem is proposed for the discrete-time multi-player systems (MPSs) with parametric uncertainties and undirected graph. The state and input constraints are considered along with the parametric uncertainties. An adaptive parameter estimator is proposed for the parametric uncertainty based on a nonlinear scheduling function. Furthermore, the cost function is constructed based on the estimated parametric uncertainties, which is used to replace the cost function of the MPSs with parametric uncertainties. An iterative algorithm is developed such that the adaptive model predictive dynamic game (AMPDG) could converge to the so-called (Formula presented.) -Nash equilibrium in a distributed manner. We establish sufficient conditions to guarantee the convergence of the proposed algorithm. In addition, the easy-to-check conditions are also provided to ensure the uniform boundedness of the studied MPSs. Finally, a numerical example of a group of spacecrafts is provided to verify the effectiveness of the proposed methodology.