A game theoretic approach to optimal control in the presence of uncertainty

The optimal control problem, in the presence of uncertainty in the plant, is formulated as a game between the uncertainty and the control variables. This approach gives an optimal control strategy which is effective even under the "worst" conditions of uncertainty. The optimal control of a second-order plant with uncertainty in frequency brings out several interesting features. In particular, the existence of a barrier demarcating the controllable and uncontrollable regions in the phase plane is revealed, which is absent in the corresponding one-sided optimization.