Joint Optimization of Information Patterns and Control in Some Linear Quadratic Gaussian Problems
A quadratic cost criterion is optimized for a discrete-time stochastic control system in which each controller uses a control law which is a linear combination of observations, as determined by the information pattern. The optimal information pattern as well as the optimal control laws are obtained for controllers with no memory. An example displaying the interplay between communication costs, control costs, and the optimum information pattern is developed. Consideration is then given to a system in which the controllers have finite memory and in which a delay is imposed on the transmission of information. This is seen to be an extension of the theory developed for the simpler case without memory.