On the worst-case disturbance of minimax optimal control

We consider a minimax optimal control problem for uncertain stochastic systems. The uncertainty in the underlying stochastic system is formulated in terms of probability measure of perturbations satisfying a relative entropy constraint. By characterizing the worst-case measure of a related stochastic minimax game, it is shown that the worst-case uncertain system can be represented in the form of a parametric perturbation of nominal system.