Infinite horizon average cost dynamic programming subject to ambiguity on conditional distribution

Ioannis Tzortzis, Charalambos D. Charalambous, Themistoklis Charalambous

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

1 Citation (Scopus)

Abstract

This paper addresses the optimality of stochastic control strategies based on the infinite horizon average cost criterion, subject to total variation distance ambiguity on the conditional distribution of the controlled process. This stochastic optimal control problem is formulated using minimax theory, in which the minimization is over the control strategies and the maximization is over the conditional distributions. Under the assumption that, for every stationary Markov control law the maximizing conditional distribution of the controlled process is irreducible, we derive a new dynamic programming recursion which minimizes the future ambiguity, and we propose a new policy iteration algorithm. The new dynamic programming recursion includes, in addition to the standard terms, the oscillator semi-norm of the cost-to-go. The maximizing conditional distribution is found via a water-filling algorithm. The implications of our results are demonstrated through an example.

Original languageEnglish
Title of host publication2015 54th IEEE Conference on Decision and Control, CDC 2015
PublisherIEEE
Pages7171-7176
Number of pages6
Volume2016-February
ISBN (Electronic)9781479978861
DOIs
Publication statusPublished - 8 Feb 2016
MoE publication typeA4 Article in a conference publication
EventIEEE Conference on Decision and Control - Osaka, Japan
Duration: 15 Dec 201518 Dec 2015
Conference number: 54

Conference

ConferenceIEEE Conference on Decision and Control
Abbreviated titleCDC
CountryJapan
CityOsaka
Period15/12/201518/12/2015

Keywords

  • Aerospace electronics
  • Dynamic programming
  • Heuristic algorithms
  • Markov processes
  • Optimal control
  • Process control

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  • Cite this

    Tzortzis, I., Charalambous, C. D., & Charalambous, T. (2016). Infinite horizon average cost dynamic programming subject to ambiguity on conditional distribution. In 2015 54th IEEE Conference on Decision and Control, CDC 2015 (Vol. 2016-February, pp. 7171-7176). [7403350] IEEE. https://doi.org/10.1109/CDC.2015.7403350