Using switching detection and variational equations for the shooting method

Pierre Martinon 1, 2 Joseph Gergaud 3
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CNRS - Centre National de la Recherche Scientifique : UMR7641, Polytechnique - X, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
Abstract : We study in this paper the resolution by single shooting of an optimal control problem with a bang-bang control involving a large number of commutations. We focus on the handling of these commutations regarding the precise computation of the shooting function and its Jacobian. We first observe the impact of a switching detection algorithm on the shooting method results. Then, we study the computation of the Jacobian of the shooting function, by comparing classical finite differences to a formulation using the variational equations. We consider as an application a low thrust orbital transfer with payload maximization. This kind of problem presents a discontinuous optimal control, and involves up to 1800 commutations for the lowest thrust. Copyright c 2000 John Wiley & Sons, Ltd.
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Optimal Control Applications and Methods, Wiley, 2007, 28 (2), pp.95-116
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Pierre Martinon, Joseph Gergaud. Using switching detection and variational equations for the shooting method. Optimal Control Applications and Methods, Wiley, 2007, 28 (2), pp.95-116. 〈inria-00271155〉

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