Linear programming estimates for Cesàro and Abel limits of optimal values in optimal control problems

Vladimir Gaitsgory, Ilya Shvartsman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We consider infinite horizon optimal control problems with time averaging and time discounting criteria and give estimates for the Cesàro and Abel limits of their optimal values in the case when they depend on the initial conditions. We establish that these limits are bounded from above by the optimal value of a certain infinite dimensional (ID) linear programming (LP) problem and that they are bounded from below by the optimal value of the corresponding dual problem. (These estimates imply, in particular, that the Cesàro and Abel limits exist and are equal to each other if there is no duality gap). In addition, we obtain IDLP-based optimality conditions for the long run average optimal control problem, and we illustrate these conditions by an example.

Original languageEnglish
Pages (from-to)1591-1610
Number of pages20
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume27
Issue number3
DOIs
Publication statusPublished - Mar 2022

Keywords

  • Optimal control
  • Cesàro and Abel limits
  • occupational measures
  • linear programming
  • duality

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