Noncooperative Model Predictive Game for Uncertain Multiagent Systems: A Dual-Mode Control Strategy
针对多智能体系统在非合作博弈中的分布式模型预测控制问题，提出一种双模控制策略，通过设计包含共识和抗干扰项的目标函数，结合二次有界引理等方法，保证系统收敛到ε-纳什均衡。
This article investigates the dual-mode distributed model predictive control (DMPC) problem for multiagent systems (MASs) in the context of noncooperative games. With regard to the mutual influence of neighbor agents, a novel objective function is developed. It consists of three main parts: the conventional quadratic function of MPC accounting for model performance and control cost, the difference between the local agent and its neighbors to guarantee the consensus, and the neighbor's disturbance to obtain the anti-interference capability. To find a nice balance between the online computational burden, practical feasibility, and model performance, a dual-model control strategy is proposed. Then, to handle the couplings resulting from the agents' communication and the negative influence caused by neighbors, the quadratic boundedness lemma, Rayleigh-Ritz theorem, and slack matrix technique are employed, and therefore, both online and offline problems with solvability are readily established. Additionally, sufficient conditions are provided for the guarantee of stability, and an iterative DMPC-based algorithm is designed to ensure that all the agents reach the $\varepsilon $ -Nash equilibrium ( $\varepsilon $ -NE). Finally, a simulation example of a spacecraft system is presented to validate the effectiveness of the proposed dual-mode DMPC, demonstrating that the spacecraft system can converge to the $\varepsilon $ -NE in a distributed manner.