Minimax optimal control of stochastic uncertain systems with relative entropy constraints

This paper considers a new class of discrete time stochastic uncertain systems in which the uncertainty is described by a constraint on the relative entropy between a nominal noise distribution and the perturbed noise distribution. This uncertainty description is a natural extension to the case of stochastic uncertain systems, of the sum quadratic constraint uncertainty description. The paper solves problems of worst case robust performance analysis and output feedback minimax optimal controller synthesis in a general nonlinear setting. Specializing these results to the linear case leads to a minimax LQG optimal controller. This controller is defined in terms of Riccati difference equations and a Kalman Filter like state equation.