Minimax and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations for Time-Delay Systems(Article)(Open Access)
- N.N. Krasovskii Institute of Mathematics and Mechanics (IMM UB RAS), Ural Federal University, Yekaterinburg, Russian Federation
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. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.
Indexed keywords
| Engineering controlled terms: | Delay control systemsDifferential equationsDynamic programmingDynamical systemsOptimal control systemsTime delayViscosity |
|---|---|
| Engineering uncontrolled terms | Cauchy problemsCoinvariant derivativeHamilton - Jacobi equationsHamilton Jacobi Bellman equationMinimaxMinimax solutionOptimal control problemOptimal controlsTime-delay systemsViscosity solutions |
| Engineering main heading: | Timing circuits |
- ISSN: 00223239
- Source Type: Journal
- Original language: English
- DOI: 10.1007/s10957-020-01742-6
- Document Type: Article
- Publisher: Springer
Plaksin, A.; N.N. Krasovskii Institute of Mathematics and Mechanics (IMM UB RAS), Ural Federal University, Yekaterinburg, Russian Federation;
© Copyright 2022 Elsevier B.V., All rights reserved.
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