Stochastic Games

该方案的基本主题是在存在多个控制器的情况下研究控制律，每个控制器都有自己的目标，每个控制器的决策影响其他控制器的信息和目标，并且每个控制器具有噪声测量，并且不一定与其他控制器的测量结果相同。整个系统是在离散时间内演化的。这类问题属于动态随机博弈论领域。考虑了两种类型的模型。首先，用具有线性噪声量测和二次代价的线性离散时间随机差分方程组描述系统的演化过程。第二种是离散时间的有限维马尔可夫链，其平均期望值代价被描述。寻求解决这些博弈问题并具有理想特性的控制律。这样的研究，除了它本身的理论意义外，在几个工程、经济或军事应用中也可能是有用的。

The basic theme of this proposal is the study of control laws in the presence of many controllers, each one of which has his own objective, the decisions of each one influence the information and objectives of the others, and where each controller has noisy measurements and not necessarily the same with those of the others. The overall system evolves in discrete time. Such problems belong to the area of Dynamic Stochastic Game Theory. Two types of models are considered. In the first, the evolution is described by linear discrete time stochastic difference equations with linear noisy measurements and quadratic costs. In the second, the evolution is described by a finite dimensions Markov chain in discrete time with average expected value costs. Control laws which solve these game problems and have desirable characteristics are sought. Such a study, besides its own theoretical interest, could be useful in several engineering economic or military applications.