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Representation of Hamilton–Jacobi Equation in Optimal Control Theory with Unbounded Control Set

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  • Arkadiusz Misztela

    (University of Szczecin)

Abstract

In this paper, we study the existence of sufficiently regular representations of Hamilton–Jacobi equations in the optimal control theory with unbounded control set. We use a new method to construct representations for a wide class of Hamiltonians. This class is wider than any constructed before, because we do not require Legendre–Fenchel conjugates of Hamiltonians to be bounded. However, in this case we obtain representations with unbounded control set. We apply the obtained results to study regularities of value functions and correlations between variational and optimal control problems.

Suggested Citation

  • Arkadiusz Misztela, 2020. "Representation of Hamilton–Jacobi Equation in Optimal Control Theory with Unbounded Control Set," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 361-383, May.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:2:d:10.1007_s10957-020-01649-2
    DOI: 10.1007/s10957-020-01649-2
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    References listed on IDEAS

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    1. Hayk Sedrakyan, 2016. "Stability of Solutions to Hamilton–Jacobi Equations Under State Constraints," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 63-91, January.
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