OPTIMAL SOLUTION TO THE SERVOMECHANISM PROBLEM FOR SYSTEMS WITH STOCHASTIC AND DETERMINISTIC DISTURBANCES

A linear-Quadratic-gaussian approach is presented to solve the servomechanism problem for systems subject to both stochastic and deterministic disturbances. A physically meaningful quadratic cost functional is defined such that it is possibleto assign desired weights to the error, to its certain derivatives, to the system effort, and to the control effort. It is shown that there existsa linear time-invariantoptimal controller if there exists a solution to the deterministic robust servomechanism problem. The resulting controlled system enjoys many properties like 'stochastic asymptotic tracking', stability, and robustness. A practical design problem is also considered to illustrate a possible application of the presented approach. © 1990 Taylor & Francis Group, LLC.