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Given a system subject to environmental fluctuations, one may ask what is the best way to change its controllable parameters in time in order to maximize, on average, a certain reward function, while steering the system between two pre-assigned states. In this work, we study the problem of optimal control for a wide class of stochastic systems, inspired by a model of an energy harvester. The stochastic noise in this system is due to the mechanical vibrations, while the reward function is the average power extracted from them. We consider the case in which the electrical resistance of the harvester can be changed in time, and we exploit the tools of control theory to work out optimal solutions in a perturbative regime, close to the stationary state. Our results show that it is possible to design protocols that perform better than any possible solution with constant resistance.<\/jats:p>","DOI":"10.3390\/e27030268","type":"journal-article","created":{"date-parts":[[2025,3,5]],"date-time":"2025-03-05T05:54:38Z","timestamp":1741154078000},"page":"268","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Optimal Control of an Electromechanical Energy Harvester"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9070-2326","authenticated-orcid":false,"given":"Dario","family":"Lucente","sequence":"first","affiliation":[{"name":"Department of Mathematics & Physics, University of Campania \u201cLuigi Vanvitelli\u201d, Viale Lincoln 5, 81100 Caserta, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6504-5523","authenticated-orcid":false,"given":"Alessandro","family":"Manacorda","sequence":"additional","affiliation":[{"name":"CNR Institute for Complex Systems, Universit\u00e0 Sapienza, P.le A. Moro 5, 00185 Rome, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9317-6862","authenticated-orcid":false,"given":"Andrea","family":"Plati","sequence":"additional","affiliation":[{"name":"Laboratoire de Physique des Solides, Universit\u00e9 Paris-Saclay CNRS, 1 Rue Nicolas Appert, 91405 Orsay, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3686-0822","authenticated-orcid":false,"given":"Alessandro","family":"Sarracino","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Campania \u201cLuigi Vanvitelli\u201d, Via Roma 29, 81031 Aversa, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3559-4032","authenticated-orcid":false,"given":"Marco","family":"Baldovin","sequence":"additional","affiliation":[{"name":"CNR Institute for Complex Systems, Universit\u00e0 Sapienza, P.le A. 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