Abstract
This paper deals with an optimal control problem of a discrete-time linear stochastic system with two controllers, each of which can make certain noisy measurements of the state of the system. These two controllers cooperate in trying to minimize the same performance index. Certain constraints are imposed on control structure, and so our problem is to determine the optimal values of the structure parameters of the controllers. Both the cases with and without information exchange between the two controllers are treated. Weak separability is introduced as an extended concept of the separation theorem and sufficient conditions for the problem to be weakly separable are obtained. Usefulness of the concept is illustrated by several numerical examples.
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