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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 Rp. 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.
Date of Publication: Aug 1979