Distributed Predictive Control Under Noncooperative Game for Systems With Switching Topology

Abstract

This paper is concerned with a distributed model predictive control (DMPC) problem for multi-agent systems (MASs) with noncooperative games under undirected switching topologies. With respect to parameter uncertainties of MASs and complicated information communication between neighbors under changing topologies, a dual-mode DMPC strategy is proposed to find a good balance between model performance, online computational burden, and initial feasible region. Specifically, to simultaneously address the stochastic mutual influences under switching topologies and the distributed decision-making in noncooperative games, a topology-mode dependent objective function in the sense of mathematical expectation is designed for each agent. Then, for the purpose of handling the deep couplings between agents and negative influence from neighbors, the quadratic bounded methodology, variable substitution method, and slack matrix technique are employed, and accordingly, a set of offline and online optimization problems with solvability is successfully established. Furthermore, by employing a Lyapunov-like function approach, sufficient conditions are obtained to ensure the achievement of $\varepsilon $ -Nash equilibrium ( $\varepsilon $ -NE), the feasibility of the proposed DMPC algorithm, and the mean-square consensus of the underlying MASs. Finally, a simulation example of a spacecraft system is presented to validate the effectiveness of the proposed DMPC. Note to Practitioners—In practical engineering, distributed industrial systems are often encountered with two challenges: time-varying communication links and the self-interested decision-making of agents. When these two issues are considered simultaneously, it is quite difficult to obtain a desirable cooperative control strategy. To address these problems, a dual-mode DMPC approach is developed for MASs under a noncooperative game with Markov switching topologies. The designed control strategy aims to find the desired topology-mode dependent controller gains and the terminal constraint set via an “offline-to-online” comprehensive optimization, so as to guarantee the mean-square consensus of the closed-loop system under switching topologies. In addition, a finite-time iterative process is introduced at each control step, enabling the agents to progressively approach and ultimately reach an $\varepsilon $ -NE. The proposed strategy can be applied to various scenarios such as uncrewed aerial vehicle swarm cooperation, distributed robotic systems, smart grids, and large-scale infrastructure networks, particularly in practical industrial environments where communication topologies change frequently, and reliable network guarantees are absent.