Linear programming approach to optimal impulse control problems with functional constraints

Alexey Piunovskiy, Yi Zhang

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
1 Downloads (Pure)

Abstract

This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple constraints on performance functionals of a similar type. Under a natural set of compactness-continuity conditions on the system primitives, we establish a linear programming approach, and prove the existence of a stationary optimal control strategy out of a more general class of randomized strategies. This is done by making use of the tools from Markov decision processes.

Original languageEnglish
Article number124817
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Volume496
Issue number2
Early online date26 Nov 2020
DOIs
Publication statusPublished - 15 Apr 2021

Bibliographical note

Funding Information:
This work was partially supported by the Royal Society International Exchanges award IE160503. The authors are grateful to Professor Alexander Plakhov from University of Aveiro (Portugal) and Institute for Information Transmission Problems (Russia) for fruitful discussions.

Publisher Copyright:
© 2020 Elsevier Inc.

Keywords

  • Constraints
  • Dynamical system
  • Impulse control
  • Linear programming
  • Markov decision process
  • Randomized strategy

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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