•  
  •  
 

Chemical Technology, Control and Management

Abstract

Stable algorithms of adaptive control, estimation of controller parameters, synthesis of adaptive control of dynamic objects by the criterion of minimum dispersion, and synthesis of suboptimal adaptive-local control of dynamic objects based on predictive models are presented. Algorithms for the stable identification of dynamic control objects based on regularization and pseudoinversion methods based on a singular decomposition are presented. Based on the use of approximations in the form of a finite sum of Gaussian distributions, recurrent identification algorithms have been developed using multiple models and adapting their parameters. Stable algorithms are proposed for identifying the parameters of an object and a controller in a closed-loop control system based on the principle of iterative regularization using the method of variational inequalities, ensuring the convergence of the desired estimates of the parameters of the object and the controller almost certainly to true values. Stable algorithms for generating control actions in locally optimal adaptive control systems for dynamic objects based on non-orthogonal factorizations and pseudoinversions of ill-conditioned or degenerate square matrices are proposed that enhance the accuracy of forming control actions in a closed control loop.

First Page

42

Last Page

49

References

1. Krasovsky A.A. 1987. The directory of the automatic control theory. Мoscow: Science.

2. Tsykunov A.M. Adaptive and robust control of dynamic objects by output. Publisher: Fizmatlit, 2009. - 268 p.

3. Igamberdiyev H., Yusupbekov A., Zaripov O., Sevinov J. Algorithms of adaptive identification of uncertain operated objects in dynamical models. Procedia Computer Science. Volume 120, 2017, Pages 854-861.

4. Igamberdiyev X.Z., Sevinov J.U., Zaripov O.O. Regulyarniye metodi i algoritmi sinteza adaptivnix system upravleniya s nastraivayemimi modelyami. -T.: TashGTU, 2014. -160 p.

5. Zybin E.Yu. On the identifiability of linear dynamic systems in a closed loop in the normal operation mode. Izvestiya SFedU. Technical science. №4 (165), 2015. -PP. 160-170.

6. Ljung L. 1991. Systems identification, p.432. The theory for the user: Translated from English. Moscow: Science.

7. Kashyap R.A., Rao A.R. Building dynamic models from experimental data. Per. from English -M.: Nauka, 1983. - 384 p.

8. Puzyrev V.A. Management of technological processes for the production of microelectronic devices. M.: Radio and communications, 1984. -160 p.

9. Kelmans G.K., Poznyak A.S., Chernitser A.V. Algorithms of “local” optimization in problems of asymptotic control of nonlinear dynamic objects // Autom. 1977. No. 11. -FROM. 73-88.

10. Neymark Yu.I., Kogan M.M., Savelyev V.P. Dynamic models of control theory. -M.: Science, 1985.

11. Igamberdiyev, H.Z; Sevinov, J.U; Yusupbekov, A.N; and Zaripov, O.O (2018) "Sustainable algorithms for synthesis of local-optimal adaptive dynamic object management systems.," Chemical Technology, Control and Management: Vol. 2018: Iss. 3, Article 14. Available at: https://uzjournals.edu.uz/ijctcm/vol2018/iss3/14.

12. Tikhonov, A., Arsenin, V. (1979) Methods of Ill-conditioned Problems Solution, p. 285. Nauka Publishers, Moscow.

13. Vainikko G.M., Veretennikov A.Yu. Iterative procedures in incorrect tasks. - M.: Nauka, 1986. - 178 p.

14. Bakushinsky A.B., Kokurin M.Yu. Iterative methods for solving irregular equations. - M.: Lenand, 2006. - 214 p.

15. Vorchik B.G. Identifiability of linear parametric stochastic systems. II. Identifiability conditions. /Automation and Remote Control, 1985, 46, 867–878.

16. Sevinov J.U. Algorithms of Sustainable Identification of Dynamic Objects in the Closed Control Line // International Journal of Innovative Technology and Exploring Engineering (IJITEE) ISSN: 2278-3075, Volume-9 Issue-2, December 2019. –PP.54-56. DOI: 10.35940/ijitee.A4842.129219.

17. Lawson C., Henson R. Numerical solution of the least squares method problems / Per. from English –M.: Science. Ch. ed. Phys.-Math. lit., 1986. –232 p.

18. Tikhonov A.N., Goncharsky A.V., Stepanov V.V., Yagola A.G. Numerical methods for solving ill-posed problems, Moscow: Nauka, 1990.

19. 19.Morozov V.A. 1987. Regular methods of the decision it is incorrect tasks in view. Moscow: Science.

20. Demmel J. Computational linear algebra. Theory and applications: Per. from English –M.: Mir, 2001 –430 s.

21. Derevitsky D.P., Fradkov A.A. Applied theory of discrete adaptive control systems. -M.: Science, 1981. - 216 p.

22. Vorсhik В.G., Fetisov V.N., Shteinberg Sh.Ye. The identification of a stochastic feedback system / Autom. Remote Control, 34:7 (1973), 1069–1081.

23. Vorchik B.G. Plant identification in a stochastic closed model / Autom. Remote Control, 36:4 (1975), 550–565.

24. 24.Bakushinskij A.B., Goncharsky A.V. 1989. Iterative approach of ill-conditioner problems solution, p.119. Moscow: Science.

25. Bodyanskiy E.V., Boryachok M.D. Locally-optimal pseudodual control of objects with unknown parameters // Autom. 1992. № 2. - PP.90-97.

26. Darkhovsky B.S. On the roughness conditions of a locally optimal stabilization system // Automation and Automation, 1988, No. 5. –C.41-50.

27. Kogan M.M., Neymark Yu.I. Functional capabilities of adaptive locally optimal control // Autom. 1994. -№6. -FROM. 94-105.

28. Degtyarev G.L., Rizaev I.S. Synthesis of locally optimal aircraft control algorithms. -M.: Mechanical Engineering, 1991. - 304 p.

29. Gantmakher F.R. Matrix theory. - M.: Nauka, 2010. - 560 p.

30. Meleshko V.I. On regularized nonorthogonal factorizations and pseudoinversions of perturbed matrices // Journal of Computational Mathematics and Mathematical Physics. Volume 26, 1986, No. 4. –C.485-498.

Included in

Engineering Commons

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.