Maximum Entropy Models, Dynamic Games, and Robust Output Feedback Control for Nonlinear Systems

In this paper, we develop a framework for designing controllers for general, partially observed discrete-time nonlinear systems which are robust with respect to uncertainties (disturbances). A general deterministic model for uncertainties is introduced, leading to a dynamic game formulation of the robust control problem. This problem is solved using an appropriate information state. We derive a partially observed nonlinear stochastic model as the maximum entropy stochastic model for the nonlinear system. A risk-sensitive stochastic control problem is formulated and solved for this partially observed stochastic model. The two problems are related using small noise limits. These small noise asymptotics are for the first time justified as the appropriate randomization, using time asymptotics of the Lagrange multipliers involved in the maximum entropy model construction. Thus for the first time a complete unification of deterministic and randomized uncertainty models is achieved. Various interpretations, consequences and applications of this unification are explained and discussed