Optimal Control of Trajectories Ensemble for a Class of Discrete Dynamic Systems

Abstract The control problems concerning the manipulation of system trajectories ensembles have received increased attention in recent years. This paper considers a class of nonlinear discrete-time systems with additive control and develops a systematic method to design optimal controls that steer an ensemble from an initial state to a terminal one minimizing the cost functional that estimates ensemble dynamics in average. Necessary optimality condition as well as functional variation are constructed. These allow building different iterative or gradient-based methods to minimize the desired control cost criterion. The motivation for this study originates from the optimization problem of advanced fuel cycle in accelerator driven system. The grand challenge here remains to address the coupled problem over the multiple cycles in the planning horizon taking into account manufacturing and nuclear data uncertainties. A brief description of physical problem and corresponding mathematical model for optimization of advanced fuel cycle in terms of the proposed approach are presented.