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 IRP. It is shown that game theoretic techniques are useful provided an incremental quadratic loss function is chosen. The optimal 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 near optimal designs and to approximate solutions to the time varying parameter case.