{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:09:07Z","timestamp":1760238547704,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,8,14]],"date-time":"2020-08-14T00:00:00Z","timestamp":1597363200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This express brief deals with the problem of the state variables regulation in the ball and beam system by applying the discrete-inverse optimal control approach. The ball and beam system model is defined by a set of four-order nonlinear differential equations that are discretized using the forward difference method. The main advantages of using the discrete-inverse optimal control to regulate state variables in dynamic systems are (i) the control input is an optimal signal as it guarantees the minimum of the Hamiltonian function, (ii) the control signal makes the dynamical system passive, and (iii) the control input ensures asymptotic stability in the sense of Lyapunov. Numerical simulations in the MATLAB environment allow demonstrating the effectiveness and robustness of the studied control design for state variables regulation with a wide gamma of dynamic behaviors as a function of the assigned control gains.<\/jats:p>","DOI":"10.3390\/sym12081359","type":"journal-article","created":{"date-parts":[[2020,8,14]],"date-time":"2020-08-14T08:28:35Z","timestamp":1597393715000},"page":"1359","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Discrete-Inverse Optimal Control Applied to the Ball and Beam Dynamical System: A Passivity-Based Control Approach"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6051-4925","authenticated-orcid":false,"given":"Oscar","family":"Danilo Montoya","sequence":"first","affiliation":[{"name":"Facultad de Ingenier\u00eda, Universidad Distrital Francisco Jos\u00e9 de Caldas, Carrera 7 No. 40B-53, Bogot\u00e1, D.C 11021, Colombia"},{"name":"Laboratorio Inteligente de Energ\u00eda, Universidad Tecnol\u00f3gica de Bol\u00edvar, km 1 v\u00eda Turbaco, Cartagena 131001, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7609-1197","authenticated-orcid":false,"given":"Walter","family":"Gil-Gonz\u00e1lez","sequence":"additional","affiliation":[{"name":"Grupo GIIEN, Facultad de Ingenier\u00eda, Instituci\u00f3n Universitaria Pascual Bravo, Campus Robledo, Medell\u00edn 050036, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carlos","family":"Ram\u00edrez-Vanegas","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias B\u00e1sicas, Universidad Tecnol\u00f3gica de Pereira, Pereira 660003, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kagami, R.M., da Costa, G.K., Uhlmann, T.S., Mendes, L.A., and Freire, R.Z. 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