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Using the Nonclassical Volterra equations of the first kind to model the developing systems

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Abstract

Proposed were integral models of the developing system with regard for various hypotheses about the ageing dynamics of its elements. The illustrative examples were accompanied by the results of calculations of the development strategies for the Russian electrical power system until 2050.

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References

  1. Glushkov, V.M., On One Class of the Dynamic Macroeconomical Models, Upravlyayushch. Sist. Mashin., 1977, no. 2, pp. 3–6.

    Google Scholar 

  2. Glushkov, V.M., Ivanov, V.V., and Yanenko, V.M., Modelirovanie razvivayushchikhsya sistem (Modeling of Developing Systems), Moscow: Nauka, 1983.

    MATH  Google Scholar 

  3. Yatsenko, Yu.P., Integral’nye modeli sistem s upravlyaemoi pamyat’yu (Integral Models of Systems with Controlled Memory), Kiev: Naukova Dumka, 1991.

    Google Scholar 

  4. Hritonenko, N. and Yatcenko, Yu., Applied Mathematical Modelling of Engineering Problems, Dordrecht: Kluwer, 1991.

    Google Scholar 

  5. Apartsin, A.S., Markova, E.V., and Trufanov, V.V., Integral Models of Development of Power Systems, Preprint of Melentiev Energy Systems Inst., Russ. Acad. Sci., Irkutsk, 2001, no. 1.

    Google Scholar 

  6. Apartsin, A.C., Karaulova, I.V., Markova, E.V., and Trufanov, V.V., Using Integral Volterra Equations to Model the Strategy of Retooling of the Power Industry, Elektrichestvo, 2005, no. 10, pp. 69–75.

    Google Scholar 

  7. Ivanov, D.V., Karaulova, I.V., Markova, E.V., Trufanov, V.V., et al., Control and Power Grid Development: Numerical Solutions, Autom. Remote Control, 2004, vol. 65, no. 3, pp. 472–482.

    Article  MathSciNet  MATH  Google Scholar 

  8. Karaulova, I.V. and Markova, E.V., Optimal Control Problem of Development of an Electric Power System, Autom. Remote Control, 2008, vol. 69, no. 4, pp. 637–644.

    Article  MathSciNet  MATH  Google Scholar 

  9. Markova, E.V., Sidler, I.V., and Trufanov, V.V., On Models of Developing Systems and Their Applications, Autom. Remote Control, 2011, vol. 72, no. 7, pp. 1371–1379.

    Article  MathSciNet  MATH  Google Scholar 

  10. Apartsin, A.S., Neklassicheskie uravneniya Volterra I roda:teoriya i chislennye metody (Nonclassical Volterra Equations of I Kind: Theory and Numerical Methods) Novosibirsk: Nauka, 1999.

    Google Scholar 

  11. Sidorov, D.N., On Solvability of the First-kind Volterra Equations with Sectionally Continuous Kernels in the Class of Generalized Functions, Izv. Irkutsk. Gos. Univ., Ser. Mat., 2012, vol. 5, no. 1, pp. 80–95.

    MathSciNet  MATH  Google Scholar 

  12. Apartsin, A.S., On the Theory of Non-Classical Volterra Equations of the First Kind, in Preprints of the 4th Int. Symp. on Inverse Problems, Design and Optimization, Albi, France, 2013.

    Google Scholar 

  13. Kantorovich, L.V. and Akilov, G.P., Funktsional’nyi analiz (Functional Analysis), Moscow: Nauka, 1977.

    Google Scholar 

  14. Apartsyn, A.S., Multilinear Volterra Equations of the First Kind, Autom. Remote Control, 2004, vol. 65, no. 2, pp. 263–269.

    Article  MathSciNet  MATH  Google Scholar 

  15. Apartsin, A.S., Polylinear Integral Volterra Equations of the First Kind: Element of Theory and Numerical Methods, Izv. Irkutsk. Gos. Univ., Ser. Mat., 2007, no. 1, pp. 13–41.

    Google Scholar 

  16. Apartsin, A.S., On Convergence of Numerical Methods for Solution of the Bilinear Volterra Equation of the First Kind, Zh. Vychisl. Mat. Mat. Fiz., 2007, no. 8, pp. 1380–1388.

    Google Scholar 

  17. Apartsin, A.S., Multilinear Volterra Equations of the First Kind and Some Problems of Control, Autom. Remote Control, 2008, vol. 69, no. 4, pp. 545–558.

    Article  MathSciNet  MATH  Google Scholar 

  18. Apartsin, A.S. and Spiryaev, V.A., On Nonimprovable Lambert-estimates of the Solutions of One Class of the Nonlinear Integral Inequalities, Tr. Inst. Mat. Mekh., UrO Ross. Akad. Nauk, 2010, vol. 16, no. 2, pp. pp. 3–12.

    Google Scholar 

  19. Apartsin, A.S., Studing the Polynomial Volterra Equation of the First Kind for Solution Stability, Autom. Remote Control, 2011, vol. 72, no. 6, pp. 1229–1236.

    Article  MathSciNet  MATH  Google Scholar 

  20. Apartsin, A.S., Polynomial Integral Volterra Equations of the First Kind and the Lambert Function, Tr. Inst. Mat. Mekh., UrO RAN, 2012, vol. 18, no. 1, pp. 69–81.

    Google Scholar 

  21. Solodusha, S.V., A Class of Systems of Bilinear Integral Volterra Equations of the First Kind of the Second Order, Autom. Remote Control, 2009, vol. 70, no. 4, pp. 663–671.

    Article  MathSciNet  MATH  Google Scholar 

  22. Solodusha, S.V., Applications of Nonlinear Volterra Equations of the Control Problem for Heat Exchange Dynamics, Autom. Remote Control, 2011, vol. 72, no. 6, pp. 1264–1270.

    Article  MathSciNet  MATH  Google Scholar 

  23. Apartsin, A.S., On an Approach to Modeling the Developing Systems, in Preprints of 6 Int. Workshop “Generalized Statements and Solutions of Control Problems,” Gelendzhik-Divnomorskoe (CD-Proc.), 2012, pp. 32–35.

    Google Scholar 

  24. “Operation and Development of Russian Power Industry in 2010,” Information and Analysis Report, Russian Power Ministry, ZAO APBE, 2011, URL:http://minenergo.gov.ru/press/doklady (application date October 11, 2012).

  25. Presentation for the Report of Minister of Power Industry A.V. Novak at the Conference at the Chairman of Russian Government D.A. Medvedev “On Upgrading Russian Power Industry until 2020,” Minenergo RF, 2012, URL: http://minenergo.gov.ru/press/doklady (application date December 11, 2012).

    Google Scholar 

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Original Russian Text © A.S. Apartsin, I.V. Sidler, 2013, published in Avtomatika i Telemekhanika, 2013, No. 6, pp. 3–16.

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Apartsin, A.S., Sidler, I.V. Using the Nonclassical Volterra equations of the first kind to model the developing systems. Autom Remote Control 74, 899–910 (2013). https://doi.org/10.1134/S0005117913060015

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