Noncooperative Model Predictive Game With Markov Jump Graph

Abstract

In this paper, the distributed stochastic model predictive control (MPC) is proposed for the noncooperative game problem of the discrete-time multi-player systems (MPSs) with the undirected Markov jump graph. To reflect the reality, the state and input constraints have been considered along with the external disturbances. An iterative algorithm is designed such that model predictive noncooperative game could converge to the so-called <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\varepsilon$</tex> -Nash equilibrium in a distributed manner. Sufficient conditions are established to guarantee the convergence of the proposed algorithm. In addition, a set of easy-to-check conditions are provided to ensure the mean-square uniform bounded stability of the underlying MPSs. Finally, a numerical example on a group of spacecrafts is studied to verify the effectiveness of the proposed method.