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Initialization of the Shooting Method via the Hamilton-Jacobi-Bellman Approach

Author

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  • E. Cristiani

    (Università di Salerno
    IAC-CNR)

  • P. Martinon

    (INRIA and CMAP École Polytechnique)

Abstract

The aim of this paper is to investigate from the numerical point of view the coupling of the Hamilton-Jacobi-Bellman (HJB) equation and the Pontryagin minimum principle (PMP) to solve some control problems. A rough approximation of the value function computed by the HJB method is used to obtain an 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.

Suggested Citation

  • E. Cristiani & P. Martinon, 2010. "Initialization of the Shooting Method via the Hamilton-Jacobi-Bellman Approach," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 321-346, August.
    • Handle: RePEc:spr:joptap:v:146:y:2010:i:2:d:10.1007_s10957-010-9649-6
    DOI: 10.1007/s10957-010-9649-6
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    References listed on IDEAS

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    1. Richard Bellman, 1954. "Some Applications of the Theory of Dynamic Programming---A Review," Operations Research, INFORMS, vol. 2(3), pages 275-288, August.
    2. F. Bonnans & P. Martinon & E. Trélat, 2008. "Singular Arcs in the Generalized Goddard’s Problem," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 439-461, November.
    3. M. Falcone, 2006. "Numerical Methods For Differential Games Based On Partial Differential Equations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 231-272.
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    Cited by:

    1. Yue Hu & Carri W. Chan & Jing Dong, 2022. "Optimal Scheduling of Proactive Service with Customer Deterioration and Improvement," Management Science, INFORMS, vol. 68(4), pages 2533-2578, April.

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