Using switching detection and variational equations for the shooting method

Pierre Martinon (1, 2) , Joseph Gergaud (3, 4)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
3 IRIT-APO - Algorithmes Parallèles et Optimisation
4 Toulouse INP - Institut National Polytechnique (Toulouse)

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.

Mots clés: Shooting method; Jacobian evaluation; switching detection; variational equations

Domaines: Optimisation et contrôle [math.OC]

Pierre Martinon, Joseph Gergaud. Using switching detection and variational equations for the shooting method. Optimal Control Applications and Methods, 2007, 28 (2), pp.95-116. ⟨inria-00271155⟩