A discrete-time differential dynamic programming algorithm with application to optimal orbit transfer

Abstract : Recently, the notion of Differential Dynamic Programming has been used to obtain new second-order algorithms for solving non-linear optimal control problems. (Unlike conventional Dynamic Programming, the Principle of Optimality is applied in the neighborhood of a nominal, non-optimal, trajectory.) A novel feature of these algorithms is that they permit strong variations in the system trajectory. In this paper, Differential Dynamic Programming is used to develop a second-order algorithm for solving discrete-time dynamic optimization problems with terminal constraints. This algorithm also utilizes strong variations and, as a result, has certain advantages over existing discrete-time methods. A non-linear computed example is presented, and comparisons are made with the results of other researchers who have solved this problem. The experience gained during the computation has suggested some extensions to an earlier, previously published Differential Dynamic Programming algorithm for continuous time problems. These extensions, and their implications are discussed. (Author)

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