Mesh refinement strategy for optimal control problems

Abstract : Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are frequently used. However, in some cases these meshes cannot cope accurately with nonlinear behavior. One way to improve the solution is to select a new mesh with a greater number of nodes. Another way, involves adaptive mesh refinement. In this case, the mesh nodes have non equidistant spacing which allow a non uniform nodes collocation. In the method presented in this paper, a time mesh refinement strategy based on the local error is developed. After computing a solution in a coarse mesh, the local error is evaluated, which gives information about the subintervals of time domain where refinement is needed. This procedure is repeated until the local error reaches a user-specified threshold. The technique is applied to solve the car-like vehicle problem aiming minimum consumption. The approach developed in this paper leads to results with greater accuracy and yet with lower overall computational time as compared to using a time meshes having equidistant spacing.
Type de document :
Communication dans un congrès
11th International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2013), 2013, Rhodes, Greece. 1558, pp.590-593, 2013, AIP Conf. Proc. 〈10.1063/1.4825560〉
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https://hal.inria.fr/hal-00917237
Contributeur : Estelle Bouzat <>
Soumis le : mercredi 11 décembre 2013 - 15:16:55
Dernière modification le : lundi 21 mars 2016 - 11:34:34

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Luis Tiago Paiva, Fernando Fontes. Mesh refinement strategy for optimal control problems. 11th International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2013), 2013, Rhodes, Greece. 1558, pp.590-593, 2013, AIP Conf. Proc. 〈10.1063/1.4825560〉. 〈hal-00917237〉

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