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Minimax and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations for Time-Delay Systems

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Abstract

The paper deals with a Bolza optimal control problem for a dynamical system, whose motion is described by a delay differential equation under an initial condition defined by a piecewise continuous function. For the value functional in this problem, the Cauchy problem for the Hamilton–Jacobi–Bellman equation with coinvariant derivatives is considered. Minimax and viscosity solutions of the Cauchy problem are studied. It is proved that both of these solutions exist, are unique, and coincide with the value functional.

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Acknowledgements

The work was performed as part of research conducted in the Ural Mathematical Center.

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Authors and Affiliations

  1. N.N. Krasovskii Institute of Mathematics and Mechanics (IMM UB RAS), Ural Federal University, Yekaterinburg, Russia

    Anton Plaksin

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  1. Anton Plaksin
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Correspondence to Anton Plaksin.

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Communicated by Nikolai Pavlovich Osmolovskii.

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Plaksin, A. Minimax and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations for Time-Delay Systems. J Optim Theory Appl 187, 22–42 (2020). https://doi.org/10.1007/s10957-020-01742-6

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  • DOI: https://doi.org/10.1007/s10957-020-01742-6

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