Geodesic
Entropy management of Gaussian stochastic systems
Journal of computational and engineering mathematics, Tome 4 (2017) no. 4, pp. 38-52.

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Two approaches to the entropy management of Gaussian stochastic system are considered. The first approach is scalar and implements the concept of "growth points". In this case the problem of maximizing (increasing) or minimizing (decreasing) the system entropy is solved. The second approach is the vector management, allowing to ensure effective changing of the entropy of two-dimensional vector, the components of which are randomness and self-organization entropies. For vector control an optimization problem on the conditional extremum is formulated. This problem can be solved using penalty methods. It is shown that the vector management of entropy for a number of cases has advantages compared to the scalar management. Examples of entropy models of real stochastic systems are provided.
Keywords: differential entropy, multidimensional random variable, Gaussian stochastic system, covariance matrix, management, randomness, self-organization. 
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A. N. Tyrsin; G. G. Gevorgyan. Entropy management of Gaussian stochastic systems. Journal of computational and engineering mathematics, Tome 4 (2017) no. 4, pp. 38-52. http://geodesic.mathdoc.fr/item/JCEM_2017_4_4_a3/

[1] I. V. Prangishvili, Entropiinye i drugie sistemnye zakonomernosti: Voprosy upravleniya slozhnymi sistemami, Nauka, M., 2003 [I. V. Prangishvili, Entropy and Other System Regularities: Control Problems of Complicated Systems, Nauka Publ., Moscow, 2010]

[2] A. Dzh. Vilson, Entropiinye metody modelirovaniya slozhnykh sistem, Fizmatlit, M., 1978 | MR

[3] S. M. Skorobogatov, Katastrofy i zhivuchest zhelezobetonnykh sooruzhenii (klassifikatsiya i elementy teorii), Uralskii gos. un-t putei soobsch., Ekaterinburg, 2009

[4] A. K. Prits, Printsip statsionarnykh sostoyanii otkrytykh sistem i dinamika populyatsii, Kaliningradskii gosudarstvennyi universitet, Kalinigrad, 1974

[5] H. Haken, Information and Self-Organization: A Macroscopic Approach to Complex Systems, Springer-Verlag, Berlin, Heidelberg, 2006 | DOI | MR | Zbl

[6] A. M. Khazen, Vvedenie mery informatsii v aksiomaticheskuyu bazu mekhaniki, RAUB, M., 1998

[7] S. A. Timashev, A. N. Tyrsin, “Entropy Approach to Risk-Analysis of Critical Infrastructure Systems”, The First International Conference on Vulnerability and Risk Analysis and Management and the Fifth International Symposium on Uncertainty Modeling and Analysis, Proceedings of the ICVRAM 2011 and ISUMA 2011 Conferences (USA, Maryland, 2011), American Society of Civil Engineers, 2011, 147–154 | DOI

[8] Yu. S. Popkov, Matematicheskaya demoekonomika: Makrosistemnyi podkhod, LENAND, M., 2013

[9] C. E. Shannon, “A Mathematical Theory of Communication”, The Bell System Technical Journal, 27:3 (1948), 379–423 | DOI | MR | Zbl

[10] T. M. Cover, J. A. Thomas, Elements of Information Theory, Wiley, New York, 1991 | MR | Zbl

[11] A. N. Tyrsin, I. S. Sokolova, “Entropiino-veroyatnostnoe modelirovanie gaussovskikh stokhasticheskikh sistem”, Matematicheskoe modelirovanie, 24:1 (2012), 88–103 | MR

[12] D. Kondepudi, I. Prigogine, Modern Thermodynamics: From Heat Engines to Dissipative Structures, Wiley, New York, 1999

[13] Yu. L. Klimontovich, Vvedenie v fiziku otkrytykh sistem, Yanus-K, M., 2002

[14] F. Perroux, L'économie du XXe siècle, Presses Universitaires de France, Paris, 1969

[15] A. N. Tyrsin, Entropiinoe modelirovanie mnogomernykh stokhasticheskikh sistem, Nauchnaya kniga, Voronezh, 2016

[16] A. N. Tyrsin, O. F. Kalev, D. A. Yashin, O. V. Lebedeva, “Otsenka sostoyaniya zdorovya populyatsii na osnove entropiinogo modelirovaniya”, Matematicheskaya biologiya i bioinformatika, 10:1 (2015), 206–219 | DOI

[17] A. V. Panteleev, T. A. Letova, Metody optimizatsii v primerakh i zadachakh, Vysshaya shkola, M., 2008