Relative Entropy Applied to Optimal Control of Stochastic Uncertain Systems on Hilbert Space

This paper considers minimax problems, in which the control minimizes the pay-off induced by a measure which maximizes the pay-off over the class of measures described by a relative entropy set between the uncertain and the true measure. We present several basic properties of the relative entropy on infinite dimensional spaces, and then we apply them to an uncertain system described by a Stochastic Differential inclusion on Hilbert space.