多智能体系统的博弈控制
Game Theoretic Control of Multi-Agent Systems
摘要：
研究了基于对策论的多智能体系统控制问题。假设一个系统级的对象是给定的，效用函数的个人代理的设计转换成一个潜在的游戏的多智能体系统。首先，对于固定拓扑，给出了基于局部信息的效用函数存在的充要条件。然后利用局部信息使系统收敛到系统目标的一个极大点，即纳什均衡。证明了网络化的进化势博弈是该多智能体系统的一个特例。其次，对于时变拓扑，利用基于状态的势博弈设计最优控制。提出了一种基于策略的马尔可夫状态转移过程，以保证基于状态的势函数的存在性。作为固定拓扑情形的推广，给出了利用局部信息的状态依赖效用函数存在的充要条件。证明了在惯性策略的作用下，系统收敛于基于状态的系统目标的最大值策略，即常返状态平衡点。
英文摘要：
Control of multi-agent systems via game theory is investigated. Assume a system level object is given, the utility functions for individual agents are designed to convert a multi-agent system into a potential game. First, for fixed topology, a necessary and sufficient condition is given to assure the existence of local information based utility functions. Then using local information the system can converge to a maximum point of the system object, which is a Nash equilibrium. It is also proved that a networked evolutionary potential game is a special case of this multi-agent system. Second, for time-varying topology, the state based potential game is utilized to design the optimal control. A strategy based Markov state transition process is proposed to assure the existence of state based potential function. As an extension of the fixed topology case, a necessary and sufficient condition for the existence of state depending utility functions using local information is also presented. It is also proved that using better reply with inertia strategy, the system converges to a maximum strategy of the state based system object, which is called the recurrent state equilibrium.
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