Toward a computationally efficient optimal solution to the LQG discrete-time dual control problem

A computationally attractive optimal solution to the discrete-time linear-quadratic-Gaussian (LQG) dual control problem in the absence of plant noise is presented. Convex vector parametric uncertainties are allowed and no a priori information is assumed save that the uncertain vector is an element of a known compact subset of R^p. It is shown that game theoretic techniques are useful provided an incremental quadratic loss function is chosen. The suboptimal solution is easily implemented since it is an average of a finite number of LQG controllers weighted by easily generated likelihood ratios. Furthermore, the structure lends itself easily to approximate solutions to the time-varying parameter case. However, further research is required to simplify the current cumbersome design procedure.