Disturbance-Observer-Based Model Predictive Control for Discrete-Time Noncooperative Game Over Undirected Graph

Abstract

In this article, the distributed model predictive control (MPC)-based noncooperative game problem is dealt with for the discrete-time multiplayer systems (MPSs) with an undirected graph. To reflect the reality, the state and input constraints are considered along with the matched disturbances and unmatched disturbances. The disturbance-observer-based composite MPC strategy is put forward which optimizes a given cost function over the receding horizon while eliminating the matched disturbances. An iterative algorithm is developed such that the model predictive dynamic game (MPDG) converges to the so-called <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon$</tex-math> </inline-formula> -Nash equilibrium in a distributed manner. Sufficient conditions are established to guarantee the convergence of the proposed algorithm. In addition, 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.