Optimal low-order controllers for linear stochastic systems

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Abstract
The design of linear controllers of reduced dimensions, which are to be used for the regulation of a class of linear stochastic systems, is dealt with. A modified quadratic performance criterion is employed in which a quadratic penalty on the system and controller states as well as on all controller gain matrices is used. Both the finite terminal time and the steady-state versions of the problem are treated, For the latter case an efficient way of deriving optimality conditions is used. For the finite terminal time problem a two-point boundary value problem whose solutions are the gain matrices of the controller is derived. For the steady-state case, two non-linear matrix algebraic equations must be solved to implement the low-order controller.

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