An Application of PL Continuation Methods to Singular Arcs Problems

Pierre Martinon () and Joseph Gergaud ()
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Pierre Martinon: UMR CNRS 5505
Joseph Gergaud: UMR CNRS 5505

A chapter in Recent Advances in Optimization, 2006, pp 163-186 from Springer

Abstract: Summary Among optimal control problems, singular arcs problems are interesting and difficult to solve with indirect methods, as they involve a multi-valued control and differential inclusions. Multiple shooting is an efficient way to solve this kind of problems, but typically requires some a priori knowledge of the control structure. We limit here ourselves to the case where the Hamiltonian is linear with respect to the control u, and primarily use a quadratic (u 2) perturbation of the criterion. The aim of this continuation approach is to obtain an approximate solution that can provide reliable information concerning the singular structure. We choose to use a PL (simplicial) continuation method, which can be more easily adapted to the multi-valued case. We will first present some convergence results regarding the continuation, and then study the numerical resolution of two example problems. All numerical experiments were conducted with the Simplicial package we developed.

Keywords: Optimal Control Problem; Differential Inclusion; Switching Function; Continuation Method; Singular Control (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-540-28258-7_11

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DOI: 10.1007/3-540-28258-0_11

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