Optimization of stochastic uncertain systems: large deviations and robustness

This paper is concerned with an abstract formulation of stochastic uncertain control systems, in which the pay-off is described by the relative entropy between the nominal measure and the uncertain measure, while the uncertain measures satisfy certain energy inequality constraints. The control seeks to maximize the minimum of the relative entropy impacted by the uncertain measure. This formulation leads to connections between minimax games arising in robust control of uncertain systems and Large Deviations theory through the so-called rate functional. In particular, certain monotonicity properties of the optimal solution are discussed, while relations to the well-known Cramer´s theorem of large deviations are introduced.