Impulsively-controlled systems and reverse dwell time: A linear programming approach

Dario Bauso*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We present a receding horizon algorithm that converges to the exact solution in polynomial time for a class of optimal impulse control problems with uniformly distributed impulse instants and governed by so-called reverse dwell time conditions. The cost has two separate terms, one depending on time and the second monotonically decreasing on the state norm. The obtained results have both theoretical and practical relevance. From a theoretical perspective we prove certain geometrical properties of the discrete set of feasible solutions. From a practical standpoint, such properties reduce the computational burden and speed up the search for the optimum thus making the algorithm suitable for the on-line implementation in real-time problems. Our approach consists in approximating the optimal impulse control problem via a binary linear programming problem with a totally unimodular constraint matrix. Hence, solving the binary linear programming problem is equivalent to solving its linear relaxation. Then, given the feasible solution from the linear relaxation, we find the optimal solution via receding horizon and local search. Numerical illustrations of a queueing system are performed. (C) 2014 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)40-51
Number of pages12
JournalNonlinear analysis-Hybrid systems
Volume16
DOIs
Publication statusPublished - May-2015
Externally publishedYes

Keywords

  • Impulse control
  • Hybrid systems
  • Reverse dwell time
  • HYBRID SYSTEMS
  • SINGLE-SERVER

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