{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:03:53Z","timestamp":1760058233912,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T00:00:00Z","timestamp":1742947200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"ELIXIR-LU"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper extends classical Markov switching models. We introduce a generalized semi-Markov switching framework in which the system dynamics are governed by an It\u00f4 stochastic differential equation. Of note, the optimal control synthesis problem is formulated for stochastic dynamic systems with semi-Markov parameters. Further, a system of ordinary differential equations is derived to characterize the Bellman functional and the corresponding optimal control. We investigate the case of linear dynamics in detail, and propose a closed-form solution for the optimal control law. A numerical example is presented to illustrate the theoretical results.<\/jats:p>","DOI":"10.3390\/sym17040498","type":"journal-article","created":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T06:58:43Z","timestamp":1742972323000},"page":"498","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimal Control of Stochastic Dynamic Systems with Semi-Markov Parameters"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1651-6402","authenticated-orcid":false,"given":"Taras","family":"Lukashiv","sequence":"first","affiliation":[{"name":"Luxembourg Centre for Systems Biomedicine, University of Luxembourg, L-4370 Belvaux, Luxembourg"},{"name":"Department of Mathematical Problems of Control and Cybernetics, Yuriy Fedkovych Chernivtsi National University, 58000 Chernivtsi, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1291-9167","authenticated-orcid":false,"given":"Igor V.","family":"Malyk","sequence":"additional","affiliation":[{"name":"Department of Mathematical Problems of Control and Cybernetics, Yuriy Fedkovych Chernivtsi National University, 58000 Chernivtsi, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7403-181X","authenticated-orcid":false,"given":"Ahmed Abdelmonem","family":"Hemedan","sequence":"additional","affiliation":[{"name":"Luxembourg Centre for Systems Biomedicine, University of Luxembourg, L-4370 Belvaux, Luxembourg"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6532-5880","authenticated-orcid":false,"given":"Venkata P.","family":"Satagopam","sequence":"additional","affiliation":[{"name":"Luxembourg Centre for Systems Biomedicine, University of Luxembourg, L-4370 Belvaux, Luxembourg"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0020-0255(73)90005-4","article-title":"Optimal control of linear stochastic systems with applications to time lag systems","volume":"5","author":"Lindquist","year":"1973","journal-title":"Inf. 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