Optimal control of linear stochastic systems with applications to time lag systems

Abstract Optimal control of linear stochastic systems of general type, perturbed by a stochastic process with independent increments, is considered. The performance functional is quadratic, and various different types of observation processes, providing either complete or incomplete information about the system, are discussed. It is shown that (with the conditions imposed) the optimal control is linear in the observed data and can be determined by solving a deterministic problem with a similar dynamic structure. These results are applied to the control of linear stochastic functional differential equations, both with complete and incomplete state information. In the latter case, a separation theorem is shown to be valid: The problem is decomposed into the corresponding deterministic control problem and a problem of estimation. The optimal feedback solution of the deterministic problem is derived.

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