On Feedback Control of Linear Stochastic Systems

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Abstract
Feedback control of linear continuous-time stochastic systems of general type is discussed. Various types of (classical) information patterns with both complete and partial observations (white and colored measurement noise) are considered. The cost functional is quadratic. A class of admissible control laws is defined which includes all linear and nonlinear control policies for which our problem makes sense, i.e., existence, uniqueness etc. are secured. Then, we determine the optimal control law by an imbedding procedure which amounts to solving a problem without a feedback loop. We investigate under what conditions the optimal control law is linear in the data.