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

Arkadiusz Misztela ()
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Arkadiusz Misztela: University of Szczecin

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 2, No 4, 383 pages

Abstract: 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.

Keywords: Hamilton–Jacobi equations; Representations of Hamiltonians; Optimal control theory; Parametrization of set-valued maps; Convex analysis; 26E25; 49L25; 34A60 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01649-2

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