Initialization of the shooting method via the Hamilton-Jacobi-Bellman approach

Emiliano Cristiani; Pierre Martinon

inria-00439543, version 1

Initialization of the shooting method via the Hamilton-Jacobi-Bellman approach

Emiliano Cristiani ()^a^, 1, Pierre Martinon ()^b^, 1, 2

Journal of Optimization Theory and Applications 146, 2 (2010) 321-346

Abstract: The aim of this paper is to investigate from the numerical point of view the possibility of coupling the Hamilton-Jacobi-Bellman (HJB) approach and the Pontryagin's Minimum Principle (PMP) to solve some control problems. We show that an approximation of the value function computed by the HJB method on rough grids can be used to obtain a good initial guess for the PMP method. The advantage of our approach over other initialization techniques (such as continuation or direct methods) is to provide an initial guess close to the global minimum. Numerical tests involving multiple minima, discontinuous control, singular arcs and state constraints are considered. The CPU time for the proposed method is less than four minutes up to dimension four, without code parallelization.

a – Ecole Nationale Supérieure de Technique Avancée
b – INRIA
1: COMMANDS (INRIA Saclay - Ile de France)
INRIA – CNRS : UMR7641 – Polytechnique - X – ENSTA ParisTech
2: Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP)
Polytechnique - X – CNRS : UMR7641

inria-00439543, version 1
http://hal.inria.fr/inria-00439543
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From: Pierre Martinon <>
Submitted on: Monday, 7 December 2009 17:43:11
Updated on: Thursday, 2 September 2010 10:42:08

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DOI: 10.1007/s10957-010-9649-6

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