On problems exhibiting a dual role of control

Some of the simplest classes of linear-quadratic-Gaussian (LQG) problems involving the dual role of control are studied. Neither analytical tools nor numerical methods are known to exist for such problems. This dual role signifies that in addition to minimizing a quadratic cost, the control explicitly determines the quality of information transmitted to the next stage. It is shown that indirect techniques (information-theoretic bounds or the construction of related zero-sum games) can be used to obtain the optimal solution for some classes of such problems; these optimal solutions are linear and can be found by solving a related parameter optimization problem. For other classes of problems it is established that nonlinear strategies indeed outperform the optimal linear strategies.