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Journal Information-measuring and Control Systems №11 for 2016 г.
Article in number:
Variational method of adaptive dynamical system identification with creation of additional invariant
Authors:
D.S. Andrashitov - Ph.D. (Eng.), Associate Professor, Moscow Vitte University (Moscow) E-mail: dima-andrahitov@rambler.ru A.A. Kostoglotov - Dr.Sc. (Eng.), Professor, Rostov State Transport University (Rostov-on-Don) E-mail: kostoglotov@icloud.com S.V. Lazarenko - Ph.D. (Eng.), Don State Technical University (Rostov-on-Don) E-mail: lazarenkosv@icloud.com I.V. Pugachev - Post-graduate Student, Don State Technical University (Rostov-on-Don) E-mail: bakut_8536@mail.ru
Abstract:
The task of the current determination of parameters of the adaptive dynamic systems from a condition of a minimum of a functionality of a discrepancy of observations is considered. The developed method of identification leads to receiving new structures of back couplings on state variables and parameters due to creation of invariants. They allow to formalize prior uncertainty of dynamics of parameters due to use of the additional properties which are shown on the true path according to a variation method which follows from been the basis for dynamics of the adaptive system and parameters of the principle of Hamilton-Ostrogradskii. Properties of variations allow to make decomposition of system of identification on subsystems of assessment of parameters and a status between which communication is defined by the equation for sensitivity function. Constructibility of the synthesized algorithms of identification is confirmed by results of the decision of the task of identification of parameters of the regulator of non-linear dynamic system. The equations of algorithms of identification differ from earlier known due to back couplings on state variables.
Pages: 55-63
References

 

  1. Lure A.I. Analiticheskaja mekhanika. M.: Gosudarstvennoe izd-vo fiz.-mat. literatury. 1961. 453 c.
  2. Kostoglotov A.A., Kostoglotov A.I., Andrashitov D.S., Lazarenko S.V. Mnogoparametricheskaja variacionnaja identifikacija dinamicheskikh sistem na osnove obedinennogo principa maksimuma // Informacionno-izmeritelnye i upravljajushhie sistemy. 2012. T. 10. № 4. S. 68-76.
  3. Kostoglotov A.A., Kostoglotov A.I., Lazarenko S.V. Mnogoparametricheskaja identifikacija konstruktivnykh parametrov metodom obedinennogo principa maksimuma // Inzhenernyjj vestnik Dona. 2011. T. 15. № 1. S. 208-218.
  4. Kostoglotov A.A., Andrashitov D.S., Derjabkin I.V., Lazarenko S.V. Variacionnyjj metod mnogoparametricheskojj identifikacii dinamicheskikh sistem na osnove iteracionnojj reguljarizacii // Uspekhi sovremennojj radioehlektroniki. 2012. № 6. S. 67-72.
  5. Andrashitov D.S., Kostoglotov A.A., Lazarenko S.V. Reguljarizirovannyjj algoritm mnogoparametricheskojj variacionnojj identifikacii dinamicheskikh sistem // Servis v Rossii i za rubezhom. 2011. № 8 (27). S. 25-36.
  6. Kostoglotov A.A., Kostoglotov A.I., Lazarenko S.V., Tsennykh B.M. Method of structural-parametric identification of Lagrangian dynamic systems in the processing of measurement information // Measurement Techniques. 2014. № 2. P. 153-159.
  7. Mironov V.I., Mironov JU.V. Metod naimenshikh kvadratov v zadachakh variacionnojj identifikacii parametrov modelejj nelinejjnykh dinamicheskikh sistem // Trudy SPIIRAN. 2009. №9. S. 148-158.
  8. Martynov B.A. Teorija kolebanijj matematicheskie modeli dinamicheskikh sistem: Ucheb. posobie. SPb. Izd-vo SPbGPU. 2002. 56 s.
  9. KHolopov S.I. Analiz relejjnojj sistemy FAPCH s obnuljaemymi integratorami // Vestnik rjazanskogo gosudarstvennogo radiotekhnicheskogo universiteta. 2011. № 38. S. 50-54.
  10. Balonin N.A., Popov O.S. Identifikacija parametrov sistem v rezhime ikh normalnogo funkcionirovanija // Avtomatika i telemekhanika. 1992. № 8. S. 98-103.
  11. Bar-Shalom Y., Rong Li X., Kirubarajan T. Estimation with Applications to Tracking and Navigation. New York: John Wiley & Sons. 2001. 558 p.
  12. Kostoglotov A.A., Kuznecov A.A., Andrashitov D.S., Derjabkin I.V., Lazarenko S.V. Iterativnye reguljarizirovannye algoritmy obrabotki izmeritelnojj informacii // Vestnik kompjuternykh i informacionnykh tekhnologijj. 2010. № 11. S. 3-9.
  13. Patent № 2362265 (RF) MPK H03H17/04, G06F17/17. Cifrovojj intellektualnyjj iterativnyjj filtr / A.A. Kostoglotov, A.A. Kuznecov, S.V. Lazarenko, A.S. Ponomarev. Zajavl. 2007142431 opubl. 20.07.09. Bjul. № 20, prioritet 16.11.2007. S 1.
  14. Khodashinsky I.A., Dudin P.A. Identification of fuzzy systems using a continuous ant colony algorithm // Optoelectronics, Instrumentation and Data Processing. 2012. № 1. P. 54-61.
  15. Kostoglotov A.A., CHebotarev A.V., Ponkratov A.I., Malyjj V.A., Prijjmakov S.N. Sistema fazovojj avtopodstrojjki chastoty v rezhime zakhvata s korrektirujushhejj petlejj avtoregulirovanija // Uspekhi sovremennojj radioehlektroniki. 2013. № 8. S. 32-36.
  16. Kostoglotov A.A., CHebotarev A.V., Cennykh B.M., Derjabkin I.V., Lazarenko S.V. Metod identifikacii parametrov dinamicheskikh sistem na osnove sovmeshhennogo s fizicheskimi principami sinteza // Nelinejjnyjj mir. 2012. T. 10. S. 801 - 809.
  17. Kostoglotov A.A., Kostoglotov A.I., Lazarenko S.V. Obedinennyjj princip maksimuma v informacionnykh tekhnologijakh analiza i sinteza. Rostov-na-Donu. 2010. 164 s.
  18. Andrashitov D.S., Kostoglotov A.A., Kostoglotov A.I., Lazarenko S.V., Cennykh B.M. Universalnyjj metod sinteza optimalnykh upravlenijj nelinejjnymi lagranzhevymi dinamicheskimi sistemami [EHlektronnyjj resurs] // Inzhenernyjj vestnik Dona. 2014. T. 28. № 1. URL: http://www.ivdon.ru/ru/magazine/issue/111 (data obrashhenija: 10.05.2016).
  19. Arutyunov A.V. Properties of the Lagrange multipliers in the Pontryagin maximum principle for optimal control problems with state constraints // Differential Equations. 2012. № 12. P. 1586-1595.