OPTIMUM DESIGN OF MEASUREMENT CHANNELS AND CONTROL POLICIES FOR LINEAR-QUADRATIC STOCHASTIC-SYSTEMS

In the design of optimal controllers for linear-quadratic stochastic s ystems, a standard assumption is that the measurement channels are fix ed and linear, and the measurement noise is Gaussian. In this paper we relax the first part of this restriction and raise the issue of the d erivation of optimum measurement structures as a part of the overall d esign. Toward this end, we take the measuement process as one given by a Wiener integral, and modify the cost function so that it now places some soft constraints on the measurement strategy. Using some results from information theory, we show that the scalar version (for both fi nite and infinite horizons) of this joint design problem admits an opt imum, dictating linear designs for both the controller and the measure ment strategy. For the vector version, however, it is possible for a n onlinear design to improve over the best linear one. In both cases, be st linear designs involve the solutions of nonlinear (deterministic) o ptimal control problems.