{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:24:01Z","timestamp":1760239441784,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,15]],"date-time":"2020-11-15T00:00:00Z","timestamp":1605398400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We revise and slightly generalize some variational problems related to the \u201cinformational approach\u201d in the classical optimization problem for automatic control systems which was popular from 1970\u20131990. We find extremals for various degenerated (derivative independent) functionals and propose some interpretations of obtained minimax relations. The main example of such functionals is given by the Gelfand\u2013Pinsker\u2013Yaglom formula for the information quantity contained in one random process in another one. We find some balance relations in a linear stationary one-dimensional system with Gaussian signal and interpret them in terms of Legendre duality.<\/jats:p>","DOI":"10.3390\/e22111300","type":"journal-article","created":{"date-parts":[[2020,11,16]],"date-time":"2020-11-16T11:04:20Z","timestamp":1605524660000},"page":"1300","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Energy\u2013Information Balance in Automatic Control Systems Revisited"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2765-0957","authenticated-orcid":false,"given":"Vladimir","family":"Rubtsov","sequence":"first","affiliation":[{"name":"D\u00e9partement de Math\u00e9matiques, LAREMA UMR 6093 du CNRS, Universit\u00e9 d\u2019Angers, 49045 Angers, France"},{"name":"Theory Division, Institute for Theoretical and Experimental Physics, 117218 Moscow, Russia"},{"name":"Institute of Geometry And Physics, 34151 Trieste, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,15]]},"reference":[{"key":"ref_1","first-page":"57","article-title":"Information criterion of optimality of automatic control systems","volume":"1","author":"Bukanov","year":"1972","journal-title":"Avtomat. Telemekh."},{"key":"ref_2","unstructured":"Pinsker, M.S. (1964). Information and Informational Stability of Random Variables and Processes, Holden-Day, Inc.. English Translation: Pinsker, M.S., Translated and edited by Amiel Feinstein."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Shannon, C. (1948). A Mathematical Theory of Communication. Bell Syst. Tech. J., 27.","DOI":"10.1002\/j.1538-7305.1948.tb01338.x"},{"key":"ref_4","unstructured":"Petrov, B.N., Petrov, V.V., Ulanov, G.M., Zaporczets, A.W., Uskov, A.S., and Kotchubievsky, l.L. (1969). Stochastic Process in Control and Information Systems, Survey Paper 63, IFAC."},{"key":"ref_5","first-page":"780","article-title":"Informational aspects of the regularization problem","volume":"195","author":"Petrov","year":"1970","journal-title":"Doklady AN SSSR"},{"key":"ref_6","first-page":"1029","article-title":"Channel capacities of feed-back informational systems with internal perturbations","volume":"194","author":"Petrov","year":"1970","journal-title":"Doklady AN SSSR"},{"key":"ref_7","unstructured":"Bukanov, N.P., Kublanov, V.S., and Rubtsov, V.N. (, January March). About a question on a synthesis of an automatic control system optimal with respect to an informational criterion. Proceedings of the All-Union Conference Optimization and Efficiency of Systems and Processes in Civil Aviation, MIIGA, Moscow, Russia. 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What Does Life Is from the Physics Point of View?, State Edition of Foreign Literature. (In Russian)."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Arnold, V.I. (1989). Mathematical Methods of Classical Mechanics, Springer. Translated by K. Vogtmann and A. Weinstein; Graduate Texts in Mathematics, 60.","DOI":"10.1007\/978-1-4757-2063-1"},{"key":"ref_14","first-page":"531","article-title":"Entropy, entropy rate and entropy stability of Gaussian random variables and processes","volume":"133","author":"Pinsker","year":"1960","journal-title":"Doklady AN SSSR"},{"key":"ref_15","first-page":"779","article-title":"Principle of developable systems","volume":"224","author":"Petrov","year":"1975","journal-title":"Doklady AN SSSR"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"840","DOI":"10.1007\/BF01341281","article-title":"On the reduction of entropy in a thermodynamic system by the intervention of intelligent beings","volume":"53","author":"Szilard","year":"1929","journal-title":"Z. Phys."},{"key":"ref_17","unstructured":"Brillouin, L. (1960). Science and Information Theory, State Edition of Foreign Literature. (In Russian)."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1119\/1.1937760","article-title":"Thermodynamics, statistics, and information","volume":"29","author":"Brillouin","year":"1961","journal-title":"Am. J. 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