LQ-based solution algorithms for discrete-time optimal control problems

This paper considers optimal control problems of a class of nonlinear discrete-time systems with respect to cost functions that are additive in the time variable. For problems without state and input constraints, a solution algorithm based on the differential dynamic programming and LQ optimal control techniques is proposed. For problems with constraints, the augmented Lagrangian method is combined with the first algorithm to form a non-primal solution algorithm. Finally, a hydroelectric generation scheduling problem is shown to fit the problem formulation, and is solved by using the algorithms developed