Receding-horizon control for max-plus linear systems with discrete actions using optimistic planning

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Abstract

This paper addresses the infinite-horizon optimal control problem for max-plus linear systems where the considered objective function is a sum of discounted stage costs over an infinite horizon. The minimization problem of the cost function is equivalently transformed into a maximization problem of a reward function. The resulting optimal control problem is solved based on an optimistic planning algorithm. The control variables are the increments of system inputs and the action space is discretized as a finite set. Given a finite computational budget, a control sequence is returned by the optimistic planning algorithm. The first control action or a subsequence of the returned control sequence is applied to the system and then a receding-horizon scheme is adopted. The proposed optimistic planning approach allows us to limit the computational budget and also yields a characterization of the level of near-optimality of the resulting solution. The effectiveness of the approach is illustrated with a numerical example. The results show that the optimistic planning approach results in a lower tracking error compared with a finite-horizon approach when a subsequence of the returned control sequence is applied.
Original languageEnglish
Title of host publicationProceedings 2016 13th International Workshop on Discrete Event Systems (WODES)
EditorsChristos G. Cassandras, Alessandro Giua, Zhiwu Li
Place of PublicationPiscataway, NJ, USA
PublisherIEEE
Pages398-403
ISBN (Print)978-1-5090-4190-0
DOIs
Publication statusPublished - 2016
Event13th International Workshop on Discrete Event Systems (WODES) - Xi'an, China
Duration: 30 May 20161 Jun 2016

Workshop

Workshop13th International Workshop on Discrete Event Systems (WODES)
Abbreviated titleWODES 2016
CountryChina
CityXi'an
Period30/05/161/06/16

Keywords

  • Planning
  • Optimal control
  • Linear systems
  • Linear programming
  • Aerospace electronics
  • Algorithm design and analysis

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