Using switching detection and variational equations for the shooting method | Zendy

Marti Pierre | Zendy; Gergaud Joseph | Zendy

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Using switching detection and variational equations for the shooting method

Author(s) -

Marti Pierre,

Gergaud Joseph

Publication year - 2007

Publication title -

optimal control applications and methods

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.458

H-Index - 44

eISSN - 1099-1514

pISSN - 0143-2087

DOI - 10.1002/oca.794

Subject(s) - shooting method , computation , thrust , maximization , optimal control , jacobian matrix and determinant , control theory (sociology) , computer science , mathematical optimization , function (biology) , payload (computing) , focus (optics) , mathematics , control (management) , algorithm , engineering , physics , aerospace engineering , artificial intelligence , mathematical analysis , computer network , evolutionary biology , network packet , biology , boundary value problem , optics

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 © 2007 John Wiley & Sons, Ltd.

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