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系统科学与数学  2007, Vol. 27 Issue (3): 464-480    DOI:
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离散时间大种群随机多智能体系统的线性二次分散动态博弈
马翠芹, 李韬, 张纪峰
中国科学院数学与系统科学研究院, 北京 100080
Linear Quadratic Decentralized Dynamic Games for Large PopulationDiscrete-Time Stochastic Multi-Agent Systems
Ma Cuiqin, Li Tao, Zhang Jifeng
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080
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摘要 研究具有耦合二次型随机性能指标的离散时间大种群随机多智能体系统的分散博弈问题.系统所受的噪声干扰为条件二阶矩有界的鞅差序列,比以往研究所考虑的高斯白噪声情形更具有广泛性.采用状态聚集方法构造了对种群状态平均的估计,基于Nash必然等价原理设计了分散控制律,并利用概率极限理论分析了闭环系统的稳定性和最优性.主要结果包括:(1)证明了对种群状态的平均的估计在某种范数意义下的强一致性,即种群状态的平均与其估计值之间的误差在该范数意义下将随系统个体数$N$的增加几乎必然收敛于0;\q (2)证明了闭环系统的几乎必然一致稳定性,即系统的稳定性与种群个体数$N$无关;(3)证明了所设计的分散控制律是几乎必然渐近Nash均衡策略.
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关键词多智能体系统   分散控制   渐近Nash均衡   离散时间系统   随机动态博弈.     
AbstractIn this paper, decentralized games of discrete-time large population stochastic multi-agent systems are considered under a coupled quadratic performance index. Based on the state aggregation method, the estimate of the population state average is constructed, with which and the Nash certainty equivalence principle, the decentralized control law is designed. By the probability limit theory, the stability and optimality of closed-loop system is analyzed. The main results
are: (1) The estimate of the PSA is shown to be strongly consistent in some norm sense, which implies that the estimation error is convergent to zero almost surely as the number of agents increases to infinity. (2) The closed-loop system is almost surely uniformly stable, in other words, the stability is independent of the number of system agents. (3) The decentralized control law is an almost surely asymptotic Nash equilibrium strategy.
Key wordsMulti-agent systems   decentralized control   asymptotic Nash equilibrium   discrete time system   stochastic dynamic game.   
收稿日期: 2007-04-29;
引用本文:   
. 离散时间大种群随机多智能体系统的线性二次分散动态博弈[J]. 系统科学与数学, 2007, 27(3): 464-480.
. Linear Quadratic Decentralized Dynamic Games for Large PopulationDiscrete-Time Stochastic Multi-Agent Systems[J]. Journal of Systems Science and Complexity, 2007, 27(3): 464-480.
 
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