A new stochastic control paradigm employing large deviations theory

This paper presents a paradigm shifting approach to the control of dynamic systems under uncertainty governed by stochastic differential equations (SDEs). Large Deviations (LD) techniques are employed to arrive at a control law for a broad class of nonlinear systems minimizing path deviations. Thereby, a shift from point-in-time to sample path statistics is suggested. A suitable formal control framework which leverages embedded Freidlin-Wentzell theory is proposed and described in detail. This includes the precise definition of the control objective and comprises an accurate discussion of the adaptation of the Freidlin-Wentzell theorem. The new control design is enabled by the transformation of an ill-posed control objective into a well-conditioned sequential optimization problem. For the first time, this allows for an LD based stochastic control design applicable to a comprehensive class of nonlinear systems. This work includes a short numerical evaluation using two benchmark problems. The proposed control paradigm allows for addressing the stochastic cost control problem as a special case. The numerical examples furnish proof of the successful design.