IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v13y2020i21p5744-d439021.html
   My bibliography  Save this article

Decompositions for MPC of Linear Dynamic Systems with Activation Constraints

Author

Listed:
  • Pedro Henrique Valderrama Bento da Silva

    (Department of Automation and Systems Engineering, Federal University of Santa Catarina, Florianópolis 88040-900, Brazil)

  • Eduardo Camponogara

    (Department of Automation and Systems Engineering, Federal University of Santa Catarina, Florianópolis 88040-900, Brazil)

  • Laio Oriel Seman

    (Department of Automation and Systems Engineering, Federal University of Santa Catarina, Florianópolis 88040-900, Brazil
    Graduate Program in Applied Computer Science, University of Vale do Itajaí, Itajaí 88302-901, Brazil)

  • Gabriel Villarrubia González

    (Expert Systems and Applications Lab, Faculty of Science, University of Salamanca, Plaza de los Caídos s/n, 37008 Salamanca, Spain)

  • Valderi Reis Quietinho Leithardt

    (COPELABS, Universidade Lusófona de Humanidades e Tecnologias, 1749-024 Lisboa, Portugal
    Departamento de Informática da Universidade da Beira Interior, 6200-001 Covilhã, Portugal
    VALORIZA, Research Center for Endogenous Resources Valorization, Instituto Politécnico de Portalegre, 7300-555 Portalegre, Portugal)

Abstract

The interconnection of dynamic subsystems that share limited resources are found in many applications, and the control of such systems of subsystems has fueled significant attention from scientists and engineers. For the operation of such systems, model predictive control (MPC) has become a popular technique, arguably for its ability to deal with complex dynamics and system constraints. The MPC algorithms found in the literature are mostly centralized, with a single controller receiving the signals and performing the computations of output signals. However, the distributed structure of such interconnected subsystems is not necessarily explored by standard MPC. To this end, this work proposes hierarchical decomposition to split the computations between a master problem (centralized component) and a set of decoupled subproblems (distributed components) with activation constraints, which brings about organizational flexibility and distributed computation. Two general methods are considered for hierarchical control and optimization, namely Benders decomposition and outer approximation. Results are reported from a numerical analysis of the decompositions and a simulated application to energy management, in which a limited source of energy is distributed among batteries of electric vehicles.

Suggested Citation

  • Pedro Henrique Valderrama Bento da Silva & Eduardo Camponogara & Laio Oriel Seman & Gabriel Villarrubia González & Valderi Reis Quietinho Leithardt, 2020. "Decompositions for MPC of Linear Dynamic Systems with Activation Constraints," Energies, MDPI, vol. 13(21), pages 1-26, November.
  • Handle: RePEc:gam:jeners:v:13:y:2020:i:21:p:5744-:d:439021
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/13/21/5744/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/1996-1073/13/21/5744/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    2. Yossiri Adulyasak & Jean-François Cordeau & Raf Jans, 2015. "Benders Decomposition for Production Routing Under Demand Uncertainty," Operations Research, INFORMS, vol. 63(4), pages 851-867, August.
    3. Shahabi, Mehrdad & Unnikrishnan, Avinash & Boyles, Stephen D., 2013. "An outer approximation algorithm for the robust shortest path problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 58(C), pages 52-66.
    4. Eduardo Conte & Paulo R. C. Mendes & Julio E. Normey-Rico, 2020. "Economic Management Based on Hybrid MPC for Microgrids: A Brazilian Energy Market Solution," Energies, MDPI, vol. 13(13), pages 1-20, July.
    5. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alejandro J. del Real & Andrés Pastor & Jaime Durán, 2021. "Generic Framework for the Optimal Implementation of Flexibility Mechanisms in Large-Scale Smart Grids," Energies, MDPI, vol. 14(23), pages 1-14, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Camilo Ortiz-Astorquiza & Ivan Contreras & Gilbert Laporte, 2019. "An Exact Algorithm for Multilevel Uncapacitated Facility Location," Transportation Science, INFORMS, vol. 53(4), pages 1085-1106, July.
    2. Hassan Zohali & Bahman Naderi & Vahid Roshanaei, 2022. "Solving the Type-2 Assembly Line Balancing with Setups Using Logic-Based Benders Decomposition," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 315-332, January.
    3. Pavlo Glushko & Csaba I. Fábián & Achim Koberstein, 2022. "An L-shaped method with strengthened lift-and-project cuts," Computational Management Science, Springer, vol. 19(4), pages 539-565, October.
    4. Gruson, Matthieu & Cordeau, Jean-François & Jans, Raf, 2021. "Benders decomposition for a stochastic three-level lot sizing and replenishment problem with a distribution structure," European Journal of Operational Research, Elsevier, vol. 291(1), pages 206-217.
    5. Dursun, Pınar & Taşkın, Z. Caner & Altınel, İ. Kuban, 2019. "The determination of optimal treatment plans for Volumetric Modulated Arc Therapy (VMAT)," European Journal of Operational Research, Elsevier, vol. 272(1), pages 372-388.
    6. Camilo Ortiz-Astorquiza & Jean-François Cordeau & Emma Frejinger, 2021. "The Locomotive Assignment Problem with Distributed Power at the Canadian National Railway Company," Transportation Science, INFORMS, vol. 55(2), pages 510-531, March.
    7. Teodor Gabriel Crainic & Mike Hewitt & Francesca Maggioni & Walter Rei, 2021. "Partial Benders Decomposition: General Methodology and Application to Stochastic Network Design," Transportation Science, INFORMS, vol. 55(2), pages 414-435, March.
    8. Nathan Sudermann‐Merx & Steffen Rebennack & Christian Timpe, 2021. "Crossing Minimal Edge‐Constrained Layout Planning using Benders Decomposition," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3429-3447, October.
    9. N. Beheshti Asl & S. A. MirHassani, 2019. "Accelerating benders decomposition: multiple cuts via multiple solutions," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 806-826, April.
    10. Kiho Seo & Seulgi Joung & Chungmok Lee & Sungsoo Park, 2022. "A Closest Benders Cut Selection Scheme for Accelerating the Benders Decomposition Algorithm," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2804-2827, September.
    11. Hu, Peng & Chu, Feng & Dolgui, Alexandre & Chu, Chengbin & Liu, Ming, 2024. "Integrated multi-product reverse supply chain design and disassembly line balancing under uncertainty," Omega, Elsevier, vol. 126(C).
    12. Denise D. Tönissen & Joachim J. Arts & Zuo-Jun Max Shen, 2021. "A column-and-constraint generation algorithm for two-stage stochastic programming problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 781-798, October.
    13. Yin, Yunqiang & Luo, Zunhao & Wang, Dujuan & Cheng, T.C.E., 2023. "Wasserstein distance‐based distributionally robust parallel‐machine scheduling," Omega, Elsevier, vol. 120(C).
    14. Muter, İbrahim & Birbil, Ş. İlker & Bülbül, Kerem, 2018. "Benders decomposition and column-and-row generation for solving large-scale linear programs with column-dependent-rows," European Journal of Operational Research, Elsevier, vol. 264(1), pages 29-45.
    15. Carvalho, Margarida & Lodi, Andrea, 2023. "A theoretical and computational equilibria analysis of a multi-player kidney exchange program," European Journal of Operational Research, Elsevier, vol. 305(1), pages 373-385.
    16. Andreas Lanz & Gregor Reich & Ole Wilms, 2022. "Adaptive grids for the estimation of dynamic models," Quantitative Marketing and Economics (QME), Springer, vol. 20(2), pages 179-238, June.
    17. Shi, Yi & Deng, Yawen & Wang, Guoan & Xu, Jiuping, 2020. "Stackelberg equilibrium-based eco-economic approach for sustainable development of kitchen waste disposal with subsidy policy: A case study from China," Energy, Elsevier, vol. 196(C).
    18. Lucio Bianco & Massimiliano Caramia & Stefano Giordani & Veronica Piccialli, 2016. "A Game-Theoretic Approach for Regulating Hazmat Transportation," Transportation Science, INFORMS, vol. 50(2), pages 424-438, May.
    19. M. Köppe & M. Queyranne & C. T. Ryan, 2010. "Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 137-150, July.
    20. Xu, Jiuping & Shu, Kejing & Wang, Fengjuan & Yang, Guocan, 2024. "Bi-level multi-objective distribution strategy integrating the permit trading scheme towards coal production capacity layout optimization: Case study from China," Resources Policy, Elsevier, vol. 91(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:13:y:2020:i:21:p:5744-:d:439021. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.