ОN APPROACHES TO THE STABILITY ANALYSIS OF NONLINEAR DYNAMIC SYSTEMS WITH LOGICAL CONTROLLERS
Abstract
The problems of modeling and of the stability analysis of nonlinear dynamic systems with logic controllers are considered. Approaches to research of stability-like properties for these systems are characterized. The aspects of application of the obtained results of analytical modeling for the elaboration of stability research algorithms and stabilization and for carrying out numerical experiments using of the modern software are described.
References
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29. Petrova S.N., Druzhinina O.V. Sintez i stabilizatsiya nechetkikh sistem upravleniya s ispol'zovaniyem parametrizovannykh lineynykh matrichnykh neravenstv // Trudy Instituta sistem¬nogo analiza RAN. Dinamika neodno¬rodnykh sistem. 2010. T. 49 (1). S. 57-61.
30. Talagayev YU.V. Analiz i sintez sverkhstoychivykh nechetkikh sistem Takagi-Sugeno // Problemy upravleniya. 2016. № 6. S. 2-11.
31. Sedova N.O., Yegrashkina ZH.Ye. Ob ispol'zovanii obshchey funktsii Lyapunova v uchebnosti sistem Takagi-Sugeno // Izvestiya Vuzov. Matematika. 2017. № 5. S. 77-85.
32. Druzhinina O.V., Masina O.N. Analiz ustoychivosti i stabilizatsii razryvnykh sistem s ispol'zovaniyem obobshchennykh funktsiy Lyapunova // Nelineynyy mir. 2014. T. 12. № 11. S. 12-22.
33. Druzhinina O.V. Indeks, divergentsiya i ustoychivost' v kachestvennoy teorii dinamicheskikh sistem. M .: Izd-vo URSS, 2013.
34. Chen K.-W. Kriticheskiy obzor parallel'nykh diskretnykh vychisleniy i kriteriy Lyapunova dlya mnozhestvennykh nechetkikh sistem s vremennoy zaderzhkoy // Inter. J. of Physical Sci. V.6. № 19. P.4492-4501.
35. Fridman Ye. Uchebnik po metodam Lyapunova dlya sistem s zaderzhkoy vremeni // European J. of Control. 2014. V.20. P.271-283.
36. Druzhinina O.V., Sedova N.O. Analiz ustoychivosti i stabilizatsii nelineynykh kaskadnykh sistem s zapazdyvaniyem v terminakh lineynykh matrichnykh neravenstv // Izvestiya RAN. Teoriya i sistemy upravleniya. 2017. № 1. S. 21-35.
37. Louson D. Dzh. Obobshchennyye protsessy Runge-Kutta dlya ustoychivykh sistem s bol'shimi lipshitsevymi konstantami // SIAM J. Numer. Anal'nyy. 1967. V. 4. № 3. S. 372-380.
38. Nikolayev S.F., Tonkov Ye.L. O nekotorykh zadachakh, svyazannykh s sushchestvovaniyem i postroyeniyem neuprezhdayushchego upravleniya dlya nestatsionarnykh upravlyayemykh sistem // Vestnik Udmurtskogo universiteta. - 2000.- T.1. - S.11-32.
39. Druzhinina O.V., Masina O.N. Sovremennyye podkhody k issledovaniyu ustoychivosti dinamicheskikh sistem s logicheskimi regulyatorami // Tez. dokl. XIII Mezhdunarodnaya konferentsiya «Ustoychivost' i kolebaniya nelineynykh sistem upravleniya» (konferentsiya Pyatnitskogo). Moskva, IPU RAN, 1-3 iyunya 2016 g. M.: IPU RAN, 2016. S. 143-145.
40. Druzhinina O.V., Masina O. N., Igonina Ye.V. Analiz upravlyayemykh dinamicheskikh sistem na osnove ispol'zovaniya TS-modeley i modifitsirovannykh lineynykh matrichnykh materialov // Materialy 19-y mezhdunarodnoy konferentsii «Raspredelennyye komp'yuternyye i telekommunikatsionnyye seti: upravleniye, vychisleniye, svyaz'» (DCCN-2016). Moskva, 21-25 noyabrya 2016 g. M.: RUDN, 2016. S. 67-74.
2. Vasil'yev S.N. K intellektnomu upravleniyu // Nelineynaya teoriya upravleniya i yeye prilozheniya. M.: Fizmatlit, 2000. S. 57-126.
3. Shestakov A.A. Obob¬shchen¬nyy pryamoy metod Lyapunova dlya sistem s raspredelennymi parametrami. M.: URSS, 2007.
4. Merenkov YU.N. Ustoychivopodobnyye svoystva differentsialnykh vklyucheniy, nechetkikh i stokhasticheskikh differentsial'nykh uravneniy. M.: Izd-vo RUDN, 2000.
5. Afanas'yev V.N. Upravleniye nelineynymi neopredelennymi dinamicheskimi ob"yektami. M.: Izd-vo URSS, 2015.
6. Pugachev V.S., Sinitsyn I.N. Teoriya stokhasticheskikh sistem. M.: Logos, 2004.
7. Sinitsyn I.N., Sinitsyn V.I. Lektsii po normal'noy i ellipsoidal'noy approksimatsii raspredeleniy v stokhasticheskikh sistemakh. M.: TORUS PRESS, 2013.
8. Pegat A. Nechetkoye modelirovaniye i upravleniye. M.: BINOM. Laboratoriya znaniy, 2009.
9. Yarushkina N.G. Nechetkiye sistemy: obzor itogov i tendentsiy razvitiya // Iskusstvennyy intellekt i prinyatiye resheniy. 2008. № 4. S. 26-38.
10. Chen G., Pham T.T. Introduction to fuzzy sets, fuzzy logic and fuzzy control systems. Boca Raton: CRC Press, 2001.
11. Driankov D., Hellendorm H., Reich Frank M. An introduction to fuzzy control. Berlin: Springer, 1996.
12. Feng G. Analysis and Synthesis of Fuzzy Control Systems: A Model-Based Approach. New York: CRC Press, 2010.
13. Lam H.-K., Leung F.H.F. Stability Analysis of Fuzzy-Model-Based Control Systems: Linear-Matrix-Inequality Approach. – Berlin: Springer, 2011.
14. Precup R.-E., Tomescu M.-L., Preitl St. Fuzzy logic control system stability analysis based on Lyapunov’s direct method // Int. J. of Computers, Communications & Control. 2009. V. IV. № 4. P. 415–426.
15. Sugeno M. On stability of fuzzy systems expressed by fuzzy rules with singleton consequents // IEEE Trans. Fuzzy Syst. 1999. V. 7. № 2. P. 201–224.
16. Takagi T., Sugeno M. Fuzzy identification of systems and its applications to modeling and control // IEEE Trans. Syst., Man and Cybernetics. 1985. V. 15. P. 116–132.
17. Tanaka K., Sugeno M. Stability analysis and design of fuzzy control systems // IEEE Trans. Fuzzy Syst. 1992. V. 45. № 2. P. 135–156.
18. Tanaka K., Wang H.O. Fuzzy control systems design and analysis: a linear matrix inequality approach. N.Y.: Wiley, 2001.
19. Wang H.O., Tanaka K., Griffin M.F. An approach to fuzzy control of nonlinear systems: stability and design issues // IEEE Trans. Fuzzy Syst. 1996. V. 4. P. 14–23.
20. Shestakov A.A., Masina O.N., Druzhinina O.V. Analiz asimptoticheskoy ustoy¬chivosti i stabilizatsii nekotorykh klassov sistem upravleniya s zapazdyvaniyem // Informatsionno-izmeritel'nyye i upravlyayushchiye sistemy. 2011. T. 9. № 12. S. 104-110.
21. Druzhinina O.V., Masina O.N. Metody issledovaniya ustoychivosti i upravlyayemosti nechetkikh i stokhasticheskikh dinamicheskikh sistem. M.: VTS RAN, 2009.
22. Masina O.N., Druzhinina O.V. Modelirovaniye i analiz ustoychivosti nekotorykh klassov sistem upravleniya. M .: VTS RAN, 2011.
23. Druzhinina O.V., Masina O.N. Metody analiza ustoychivosti dinamicheskikh sistem intellektnogo upravleniya. M .: URSS, 2015.
24. Druzhinina O.V., Igonina Ye.V., Masina O.N. Modelirovaniye i stabilizatsiya dinamicheskikh sistem s logicheskimi regulyatorami / soobshcheniyami po prikladnoy matematike. M .: VTS RAN, 2015.
25. Druzhinina O.V., Masina O.N. Algoritmy stabilizatsii diskretnoy upravlyayemoy sistemy s singlton-vykhodom // Informatsionno-izmeritel'nyye i upravlyayushchiye sistemy. 2012. T. 10. № 12. S. 35-41.
26. Druzhinina O.V., Masina O.N., Igonina Ye.V. Razrabotka algoritmov stabilizatsii upravlyayemykh sistem na osnove svoystv lineynykh matrichnykh neravenstv // Naukoyemkiye tekhnologii. 2013. T. 14. № 6. S. 4-8.
27. Yegrashkina ZH.Ye., Sedova N.O. Ustoychivost' i stabilizatsiya neli¬neynykh sistem obyknovennykh differentsial'nykh uravneniy v terminakh lineynykh matrichnykh neravenstv // Nelineynyy mir. 2015. T. 13. № 1. S. 3-15.
28. Masina O.N., Druzhinina O.V., Afanas'yeva V.I. Analiz ustoychivosti diskretnykh sistem upravleniya na osnove funktsiy Lyapunova i svoystva lineynykh matrichnykh neravenstv // Informatsionno-izmeritel'nyye i upravlyayushchiye sistemy. 2011. T. 9. № 7. S. 53-62.
29. Petrova S.N., Druzhinina O.V. Sintez i stabilizatsiya nechetkikh sistem upravleniya s ispol'zovaniyem parametrizovannykh lineynykh matrichnykh neravenstv // Trudy Instituta sistem¬nogo analiza RAN. Dinamika neodno¬rodnykh sistem. 2010. T. 49 (1). S. 57-61.
30. Talagayev YU.V. Analiz i sintez sverkhstoychivykh nechetkikh sistem Takagi-Sugeno // Problemy upravleniya. 2016. № 6. S. 2-11.
31. Sedova N.O., Yegrashkina ZH.Ye. Ob ispol'zovanii obshchey funktsii Lyapunova v uchebnosti sistem Takagi-Sugeno // Izvestiya Vuzov. Matematika. 2017. № 5. S. 77-85.
32. Druzhinina O.V., Masina O.N. Analiz ustoychivosti i stabilizatsii razryvnykh sistem s ispol'zovaniyem obobshchennykh funktsiy Lyapunova // Nelineynyy mir. 2014. T. 12. № 11. S. 12-22.
33. Druzhinina O.V. Indeks, divergentsiya i ustoychivost' v kachestvennoy teorii dinamicheskikh sistem. M .: Izd-vo URSS, 2013.
34. Chen K.-W. Kriticheskiy obzor parallel'nykh diskretnykh vychisleniy i kriteriy Lyapunova dlya mnozhestvennykh nechetkikh sistem s vremennoy zaderzhkoy // Inter. J. of Physical Sci. V.6. № 19. P.4492-4501.
35. Fridman Ye. Uchebnik po metodam Lyapunova dlya sistem s zaderzhkoy vremeni // European J. of Control. 2014. V.20. P.271-283.
36. Druzhinina O.V., Sedova N.O. Analiz ustoychivosti i stabilizatsii nelineynykh kaskadnykh sistem s zapazdyvaniyem v terminakh lineynykh matrichnykh neravenstv // Izvestiya RAN. Teoriya i sistemy upravleniya. 2017. № 1. S. 21-35.
37. Louson D. Dzh. Obobshchennyye protsessy Runge-Kutta dlya ustoychivykh sistem s bol'shimi lipshitsevymi konstantami // SIAM J. Numer. Anal'nyy. 1967. V. 4. № 3. S. 372-380.
38. Nikolayev S.F., Tonkov Ye.L. O nekotorykh zadachakh, svyazannykh s sushchestvovaniyem i postroyeniyem neuprezhdayushchego upravleniya dlya nestatsionarnykh upravlyayemykh sistem // Vestnik Udmurtskogo universiteta. - 2000.- T.1. - S.11-32.
39. Druzhinina O.V., Masina O.N. Sovremennyye podkhody k issledovaniyu ustoychivosti dinamicheskikh sistem s logicheskimi regulyatorami // Tez. dokl. XIII Mezhdunarodnaya konferentsiya «Ustoychivost' i kolebaniya nelineynykh sistem upravleniya» (konferentsiya Pyatnitskogo). Moskva, IPU RAN, 1-3 iyunya 2016 g. M.: IPU RAN, 2016. S. 143-145.
40. Druzhinina O.V., Masina O. N., Igonina Ye.V. Analiz upravlyayemykh dinamicheskikh sistem na osnove ispol'zovaniya TS-modeley i modifitsirovannykh lineynykh matrichnykh materialov // Materialy 19-y mezhdunarodnoy konferentsii «Raspredelennyye komp'yuternyye i telekommunikatsionnyye seti: upravleniye, vychisleniye, svyaz'» (DCCN-2016). Moskva, 21-25 noyabrya 2016 g. M.: RUDN, 2016. S. 67-74.
Published
2017-08-18
How to Cite
ДРУЖИНИНА, Ольга Валентиновна; МАСИНА, Ольга Николаевна.
ОN APPROACHES TO THE STABILITY ANALYSIS OF NONLINEAR DYNAMIC SYSTEMS WITH LOGICAL CONTROLLERS.
Modern Information Technologies and IT-Education, [S.l.], v. 13, n. 2, p. 40-49, aug. 2017.
ISSN 2411-1473. Available at: <http://sitito.cs.msu.ru/index.php/SITITO/article/view/234>. Date accessed: 03 july 2024.
doi: https://doi.org/10.25559/SITITO.2017.2.234.
Section
Theoretical Questions of Computer Science, Computer Mathematics
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