Representation of Weak Solutions of Convex Hamilton–Jacobi–Bellman Equations on Infinite Horizon

Vincenzo Basco ()
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Vincenzo Basco: The University of Melbourne

Journal of Optimization Theory and Applications, 2020, vol. 187, issue 2, No 4, 370-390

Abstract: Abstract In the present paper, it is provided a representation result for the weak solutions of a class of evolutionary Hamilton–Jacobi–Bellman equations on infinite horizon, with Hamiltonians measurable in time and fiber convex. Such Hamiltonians are associated with a—faithful—representation, namely involving two functions measurable in time and locally Lipschitz in the state and control. Our results concern the recovering of a representation of convex Hamiltonians under a relaxed assumption on the Fenchel transform of the Hamiltonian with respect to the fiber. We apply them to investigate the uniqueness of weak solutions, vanishing at infinity, of a class of time-dependent Hamilton–Jacobi–Bellman equations. Assuming a viability condition on the domain of the aforementioned Fenchel transform, these weak solutions are regarded as an appropriate value function of an infinite horizon control problem under state constraints.

Keywords: Hamilton–Jacobi–Bellman equations; Weak solutions; Infinite horizon; State constraints; Representation of Hamiltonians; 70H20; 49L25; 49J24; 35E10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01763-1

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