Bauso, D. (2009) Optimal impulse control problems and linear programming. In: Proceedings of the 48th IEEE Conference on Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, December 16-18, 2009, Shanghai, P.R. China. IEEE , 5299 - 5304. ISBN 978-1-4244-3871-6
Abstract
Optimal impulse control problems are, in general, difficult to solve. A current research goal is to isolate those problems that lead to tractable solutions. In this paper, we identify a special class of optimal impulse control problems which are easy to solve. Easy to solve means that solution algorithms are polynomial in time and therefore suitable to the on-line implementation in real-time problems. We do this by using a paradigm borrowed from the Operations Research field. As main result, we present a solution algorithm that converges to the exact solution in polynomial time. 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. It turns out that any solution of the linear relaxation is a feasible solution for the optimal impulse control problem. Then, given the feasible solution, obtained solving the linear relaxation, we find the optimal solution via local search.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works |
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: | 29 Jan 2016 15:26 |
Last Modified: | 28 Mar 2018 02:34 |
Published Version: | http://dx.doi.org/10.1109/CDC.2009.5399855 |
Status: | Published |
Publisher: | IEEE |
Refereed: | Yes |
Identification Number: | 10.1109/CDC.2009.5399855 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:89745 |