In a control system, the control is closely related to information. The information is utilized not only to estimate the state of the system but to control the system. The control affects the information and the information itself is dependent on the control in the past. A large system may have many controllers, and they can not in general share the same information. They act on decisions derived from different bits of information, and their actions influence one another. This interplay of information and control results from the feedback paths among the controllers.
In this paper, the relation between information and control is discussed in the linear-Gaussian team problems with general nonclassical information pattern. In this pattern, each controller is given different imperfect information. It is proved that there exist the optimal controls for this team problem. Under certain conditions, the optimal controls become the functions of only the state variables of the finite dimensional estimators. It is shown that in a hierarchical information pattern, the linear optimal control law satisfies the separation theorem.
The linear-quadratic-Gaussian team problem with one-step delayed sharing information pattern is discussed. Then the optimal control laws are given by the linear combination of the state variables of finite dimensional estimators. This decentralized information pattern can be converted to the other type of the decentralized, the centralized or the classical information pattern by transmitting or communicating the information among the controllers. The optimal control laws and the transmission or communication laws for the time-variant information pattern are derived by considering both the payoff and the information cost.
The above results can be applicable to the analysis and the design of the large scale information systems such as the computer network system, the economic system and so on.
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