Chance-constrained model predictive controller synthesis for stochastic max-plus linear systems

V. Rostampour Samarin, Dieky Adzkiya, Sadegh Esmaeil Zadeh Soudjani, Bart De Schutter, Tamas Keviczky

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

1 Citation (Scopus)

Abstract

This paper presents a stochastic model predictive control problem for a class of discrete event systems, namely stochastic max-plus linear systems, which are of wide practical interest as they appear in many application domains for timing
and synchronization studies. The objective of the control problem is to minimize a cost function under constraints on states, inputs and outputs of such a system in a receding horizon fashion. In contrast to the pessimistic view of the robust approach on uncertainty, the stochastic approach interprets the constraints probabilistically, allowing for a sufficiently small violation probability level. In order to address the resulting nonconvex chance-constrained optimization problem, we present two ideas in this paper. First, we employ a scenario-based approach to approximate the problem solution, which optimizes the control inputs over a receding horizon, subject to the constraint satisfaction under a finite number of scenarios of the uncertain parameters. Second, we show that this approximate optimization problem is convex with respect to the decision variables and we provide a-priori probabilistic guarantees for the desired level of
constraint fulfillment. The proposed scheme improves the results in the literature in two distinct directions: we do not require any assumption on the underlying probability distribution of the system parameters; and the scheme is applicable to high dimensional problems, which makes it suitable for real industrial applications. The proposed framework is demonstrated on a twodimensional production system and it is also applied to a subset
of the Dutch railway network in order to show its scalability and study its limitations.
Original languageEnglish
Title of host publicationProceedings of the 2016 IEEE International Conference on Systems, Man, and Cybernetics
Place of PublicationPiscataway, NJ, USA
PublisherIEEE
Pages3581-3588
ISBN (Electronic)9781509018970
DOIs
Publication statusPublished - 2016
Event2016 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2016 - Budapest, Hungary
Duration: 9 Oct 201612 Oct 2016

Conference

Conference2016 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2016
CountryHungary
CityBudapest
Period9/10/1612/10/16

Keywords

  • Multiprotocol label switching
  • Stochastic processes
  • Probabilistic logic
  • Uncertainty
  • Optimization
  • Rail transportation
  • Algebra

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