Linear programming approach to deterministic infinite horizon optimal control problems with discounting

Vladimir Gaitsgory*, Marc Quincampoix

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

63 Citations (Scopus)

Abstract

We investigate relationships between the determ inistic infinite time horizon optimal control problem with discounting, in which the state trajectories remain in a given compact set Y, and a certain infinite dimensional linear programming (IDLP) problem. We introduce the problem dual with respect to this IDLP problem and obtain some duality results. We construct necessary and sufficient optimality conditions for the optimal control problem under consideration, and we give a characterization of the viability kernel of Y. We also indicate how one can use finite dimensional approximations of the IDLP problem and its dual for construction of near optimal feedback controls. The construction is illustrated with a numerical example.

Original languageEnglish
Pages (from-to)2480-2512
Number of pages33
JournalSIAM Journal on Control and Optimization
Volume48
Issue number4
DOIs
Publication statusPublished - 2009
Externally publishedYes

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