Bauso, D. (2015) Impulsively-controlled systems and reverse dwell time: A linear programming approach. Nonlinear Analysis: Hybrid Systems, 16. 40 - 51. ISSN 1751-570X
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014 Elsevier Ltd. This is an author produced version of a paper subsequently published in Nonlinear Analysis: Hybrid Systems. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/) |
Keywords: | Impulse control; Hybrid systems; Reverse dwell time |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 08 Oct 2015 15:33 |
Last Modified: | 23 Dec 2016 19:53 |
Published Version: | http://dx.doi.org/10.1016/j.nahs.2014.11.004 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.nahs.2014.11.004 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:89653 |