Semigroup Theory for Dual Dynamic Programming

Authors

  • Naseif Jasim Al –Jawar Department of Mathematics, College of Science, University of Al –Mustansiriyah. Baghdad –Iraq
  • Dyaina hilaS Al–Anbagi Department of Mathematics, College of Science, University of Al –Mustansiriyah. Baghdad –Iraq

Keywords:

Dual value function, Dual dynamic programming, semigroup theory, HJB equation, Dual optimal feedback control

Abstract

In this paper, the nonclassical approach to dynamic programming for the optimal control problem via strongly continuous semigroup has been presented. The dual value function VD ( .,. ) of the problem is defined and characterized. We find that it satisfied the dual dynamic programming principle and dual Hamilton Jacobi –Bellman equation. Also, some properties of VD (. , .) have been studied, such as, various kinds of continuities and boundedness, these properties used to give a sufficient condition for optimality. A suitable verification theorem to find a dual optimal feedback control has been proved. Finally gives an example which illustrates the value of the theorem which deals with the sufficient condition for optimality.

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Published

2023-04-30

Issue

Section

Mathematics

How to Cite

Semigroup Theory for Dual Dynamic Programming. (2023). Iraqi Journal of Science, 56(2B), 1471-1488. https://ijs.uobaghdad.edu.iq/index.php/eijs/article/view/10157

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