{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:21:59Z","timestamp":1760239319620,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T00:00:00Z","timestamp":1604275200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"PLATAFORMA DE VEH\u00cdCULOS DE  TRANSPORTE DE MATERIALES Y SEGUIMIENTO AUT\u00d3NOMO","award":["SA063G19"],"award-info":[{"award-number":["SA063G19"]}]},{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["Finance Code 001"],"award-info":[{"award-number":["Finance Code 001"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/04111\/2020"],"award-info":[{"award-number":["UIDB\/04111\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Energies"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/en13215744","type":"journal-article","created":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T19:51:31Z","timestamp":1604346691000},"page":"5744","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Decompositions for MPC of Linear Dynamic Systems with Activation Constraints"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8394-9582","authenticated-orcid":false,"given":"Pedro Henrique","family":"Valderrama Bento da Silva","sequence":"first","affiliation":[{"name":"Department of Automation and Systems Engineering, Federal University of Santa Catarina, Florian\u00f3polis 88040-900, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0236-0689","authenticated-orcid":false,"given":"Eduardo","family":"Camponogara","sequence":"additional","affiliation":[{"name":"Department of Automation and Systems Engineering, Federal University of Santa Catarina, Florian\u00f3polis 88040-900, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6806-9122","authenticated-orcid":false,"given":"Laio Oriel","family":"Seman","sequence":"additional","affiliation":[{"name":"Department of Automation and Systems Engineering, Federal University of Santa Catarina, Florian\u00f3polis 88040-900, Brazil"},{"name":"Graduate Program in Applied Computer Science, University of Vale do Itaja\u00ed, Itaja\u00ed 88302-901, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6536-2251","authenticated-orcid":false,"given":"Gabriel","family":"Villarrubia Gonz\u00e1lez","sequence":"additional","affiliation":[{"name":"Expert Systems and Applications Lab, Faculty of Science, University of Salamanca, Plaza de los Ca\u00eddos s\/n, 37008 Salamanca, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0446-9271","authenticated-orcid":false,"given":"Valderi","family":"Reis Quietinho Leithardt","sequence":"additional","affiliation":[{"name":"COPELABS, Universidade Lus\u00f3fona de Humanidades e Tecnologias, 1749-024 Lisboa, Portugal"},{"name":"Departamento de Inform\u00e1tica da Universidade da Beira Interior, 6200-001 Covilh\u00e3, Portugal"},{"name":"VALORIZA, Research Center for Endogenous Resources Valorization, Instituto Polit\u00e9cnico de Portalegre, 7300-555 Portalegre, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"740","DOI":"10.1016\/j.jprocont.2013.09.024","article-title":"Process Control Efficient Building Energy Management Using Distributed Model Predictive Control","volume":"24","author":"Scherer","year":"2013","journal-title":"J. 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