BSU Bulletin. Mathematics, Informatics
Bibliographic description:
, VECTOR ENTROPY MONITORING AND CONTROL OF GAUSSIAN STOCHASTIC SYSTEMS // BSU Bulletin. Mathematics, Informatics. - 2018. №1. . - С. 19-33.
Title:
VECTOR ENTROPY MONITORING AND CONTROL OF GAUSSIAN STOCHASTIC SYSTEMS
Financing:
Работа выполнена при финансовой поддержке гранта РФФИ, проект № 17-01-00315а
Codes:
Annotation:
The article deals with the vector approach of entropy monitoring and con- trol. It is the representation of differential entropy of a multidimensional sto- chastic system as a two-dimensional vector, the components of which are the entropies of randomness and self-organization. The system state is evaluated simultaneously with these two components. Vector control enables efficient entropy change as a two-dimensional vector, the components of which are the entropies of randomness and self-organization. We have formulated an optimi- zation extremum problem for the important case of Gaussian stochastic sys- tems. This problem can be solved by penalty function methods. It is shown that in a number of cases vector entropy control has advantages in comparison with scalar control. We give the examples of entropy monitoring and control for real stochastic systems.
Keywords:
differential entropy; model; multidimensional random variable; Gaussian stochastic system; covariance matrix; monitoring; control; random- ness; self-organization.
List of references:
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Panteleev A. V., Letova T. A. Metody optimizatsii v primerakh i zada- chakh [Methods of Optimization in Examples and Problems]. 3nd ed. Moscow: Vysshaya shkola Publ., 2008. 544 p.
Wilson A. J. Entropiinye metody modelirovaniya slozhnykh sistem [En- tropy Methods of Modeling Complex Systems]. Moscow: Nauka Publ.,1978. (Russian translation).
Skorobogatov S. M. Katastrofy i zhivuchest' zhelezobetonnykh sooruzhenii (klassifikatsiya i elementy teorii) [Catastrophes and Survivability of Rein- forced Concrete Structures (classification and the theory elements). Ekaterin- burg: Ural State University of Railway Transport Publ., 2009. 512 p.
Prits A. K. Printsip statsionarnykh sostoyanii otkrytykh sistem i dinamika populyatsii [Principle of Steady States of Open Systems and the Dynamics of Population]. Kalinigrad: Kaliningrad State University Publ., 1974. 124 p.
Haken H. Information and Self-Organization: A Macroscopic Approach to Complex Systems. Springer-Verlag, 1988.
Khazen A. M. Vvedenie mery informatsii v aksiomaticheskuyu bazu mek- haniki [Introduction of Information Measure in the Axiomatic Basis of Me- chanics]. 2nd ed. Moscow: Raub Publ., 1998. 168 p.
Popkov Yu. S. Matematicheskaya demoekonomika: Makrosistemnyi podkhod [Mathematical Demoeconomy: Macrosystem Approach]. Moscow: Lenand, 2013. 560 p.
Shannon C. E. A Mathematical Theory of Communication. The Bell Sys- tem Technical Journal. 1948. V. 27. No. 3. Pp. 379–423; No. 4. Pp. 623–656.
Tyrsin A. N. Entropiinoe modelirovanie mnogomernykh stokha- sticheskikh system [Entropy Modeling of Multidimensional Stochastic Sys- tems]. Voronezh: Nauchnaya kniga Publ., 2016. 156 p.
Tyrsin A. N., Sokolova I. S. Entropiino-veroyatnostnoe modelirovanie gaussovskikh stokhasticheskikh sistem [Entropy Probabilistic Modeling of Gaussian Stochastic Systems]. Matematicheskoe modelirovanie — Mathemati- cal Modeling. 2012. V. 24. No. 1. Pp. 88–103.
Klimontovich Yu. L. Vvedenie v fiziku otkrytykh system [Introduction to Open Systems Physics]. Moscow: Yanus-K Publ., 2002. 284 p.
Regiony Rossii. Osnovnye sotsial'no-ekonomicheskie pokazateli goro- dov [Regions of Russia. Key Socio-Economic Indicators of Cities]. Feder- al'naya sluzhba gosudarstvennoi statistiki, Rosstat — Federal Service of State Statistics, Rosstat. Available at: http://www.gks.ru/wps/wcm/connect/rosstat_main/rosstat/ru/statistics/publicati ons/catalog/ (accessed 15.02.2018)
Panteleev A. V., Letova T. A. Metody optimizatsii v primerakh i zada- chakh [Methods of Optimization in Examples and Problems]. 3nd ed. Moscow: Vysshaya shkola Publ., 2008. 544 p.
Article.pdf