PROCEDURE FORMALIZATION FOR CONSTRUCTING AN ADAPTIVE CONTROL SYSTEM WITH A REFERENCE MODEL BASED ON THE LYAPUNOV FUNCTION

Authors

Tulkin Vafoqulovich Botirov, Navoi State Mining Institute Address: 27 G`alaba shoh street, 210100, Navoi city, Republic of Uzbekistan E-mail: btv1979@mail.ru, Phone:+998-94-218-43-67;Follow

Abstract

Discusses the formalization of the procedure for constructing an adaptive control system with a reference model based on the Lyapunov function. It is shown that the asymptotic stability of the extended system of differential equations guarantees accurate tracking of the desired output signal of the model. At the same time, the expediency of analyzing the asymptotic stability of the system in extended space using the Lyapunov function is shown. The above algorithms help to stabilize the computational matrix inversion procedure and thereby increase the accuracy of estimating the adjustable parameter in an adaptive control system.

First Page

45

Last Page

48

References

1. V.B.Yakovlev, Adaptivnie sistemi avtomaticheskogo upravleniya [Adaptive automatic control systems]. Leningrad: Izd-vo Leningr. un-ta, 1984, 204 p. (in Russian).
2. V.N.Fomin, A.L.Fradkov, V.A.Yakubovich, Adaptivnoe upravlenie dinamicheskimi ob'ektami [Adaptive management of dynamic objects]. Moskva: Nauka, 1981, 448 p. (in Russian).
3. S.D.Zemlyakov, V.Yu.Rutkovskiy, A.V.Silaev, “Nastraivaemaya funksional'naya rabotosposobnost' adaptivnix sistem s etalonnoy model'yu” [Configurable functional performance of an adaptive system with a reference model], Avtomatika i telemexanika, no. 6, pp. 125-134, 1997 (in Russian).
4. V.I.Pugachev, “Issledovanie vozmojnostey adaptivnoy sistemi upravleniya s etalonnoy model'yu” [A study of the possibilities of adaptive control system with reference model], Izvestiya vuzov. Pishevaya texnologiya, no. 2, pp. 80-83, 2007 (in Russian).
5. I.V.Miroshnik, V.O.Nikiforov, A.L.Fradkov, Nelineynoe i adaptivnoe upravlenie slojnimi dinamicheskimi sistemami [Nonlinear and adaptive control systems for complex dynamic systems]. Sankt-Peterburg: Nauka, 2000, 549 p. (in Russian).
6. Nadirbek Yusupbekov, “Knowledge-Based Planning for Industrial Automation Systems: The Way to Support Decision Making”, 13th International Conference On Theory And Application Of Fuzzy Systems And Soft Computing - ICAFS-2019, 2019, DOI.ORG/10.1007/978-3-030-04164-9_115.
7. A.G.Aleksandrov, Adaptivnoe upravlenie s etalonnoy model'yu pri vneshnix vozmusheniyax [Adaptive control with a reference model under external influences], Avtomatika i telemexanika, no. 5, pp. 77–90, 2004 (in Russian).
8. A.G.Aleksandrov, Optimal'nie i adaptivnie sistemi [Optimal and adaptive structure]. Moskva: Nauka, 2003, 278 p. (in Russian).
9. A.M.Sikunov, Adaptivnoe i robastnoe upravlenie dinamicheskimi ob'ektami po vixodu [Adaptive and regional control of dynamic objects by output]. Moskva: Nauka, 2008, 180 p. (in Russian).
10. N.R.Yusupbekov, H.Z.Igamberdiev, U.F.Mamirov, “Algorithms of Sustainable Estimation of Unknown Input Signals in Control Systems”, Journal of Automation, Mobile Robotics & Intelligent Systems, vol. 12(4), pp. 83-86, 2018, DOI: 10.14313/JAMRIS_4-2018/29.
11. H.Z.Igamberdiyev, J.U.Sevinov, A.N.Yusupbekov, and O.O.Zaripov, “Sustainable algorithms for synthesis of local-optimal adaptive dynamic object management systems”, Chemical Technology, Control and Management, vol. 2018, Iss. 3, Article 14, 2018, https://uzjournals.edu.uz/ijctcm/vol2018/iss3/14.
12. G.S.Aksenov, V.N.Fomin, “Sintez adaptivnix regulyatorov na osnove metoda funksii Lyapunova” [Synthesis of adaptive regulators based on the Lyapunov function method], Avtomatika i telemexanika, no. 6, pp. 126–137, 1982 (in Russian).
13. A.M.Pishuxin, G.F.Axmed'yanova, “Stupenchatoe adaptivnoe upravlenie s etalonnoy model'yu” [Step-by-step adaptive control with a reference model], Izvestiya Samarskogo nauchnogo sentra Rossiyskoy akademii nauk, vol. 19, no. 1, pp. 157-161, 2017 (in Russian).
14. V.A.Beynarovich, “Samonastraivayushiesya sistemi s etalonnoy model'yu” [Self-tuning systems with a reference model], Dokladi TUSURa, no. 1 (21), pp. 67-69, 2010 (in Russian).
15. A.A.Shilin, “Adaptivniy nelineyniy regulyator s etalonnoy model'yu” [The nonlinear adaptability of the regulatory reference model], Dokladi TUSURa, pp. 181-184, 2004.
16. F.R.Gantmacher, J.L.Brenner, “Applications of the Theory of Matrices”, Courier Corporation, 2005.
17. R.A.Horn, C.R.Johnson, Matrix analysis, Cambridge University Express, 1985.
18. A.I.Jdanov, Vvedenie v metodi resheniya nekorrektnix zadach [Introduction to methods for solving incorrect problems]. Samara: Samarskogo gos. aerokosmicheskogo un-ta, 2006, 87 p. (in Russian).
19. A.N.Tixonov, V.Ya.Arsenin, Metodi resheniya nekorrektnix zadach [Methods for solving incorrect problems]. Moskva: Nauka, 1986, 288 p. (in Russian).
20. A.F.Verlan', V.S.Sizikov, Integral'nie uravneniya: metodi, algoritmi, programmi [Integral equations: methods, algorithms, programs]. Kiev: Naukova dumka, 1986, 542 p. (in Russian).

Recommended Citation

Botirov, Tulkin Vafoqulovich (2020) "PROCEDURE FORMALIZATION FOR CONSTRUCTING AN ADAPTIVE CONTROL SYSTEM WITH A REFERENCE MODEL BASED ON THE LYAPUNOV FUNCTION," Chemical Technology, Control and Management: Vol. 2020: Iss. 3, Article 8.
DOI: https://doi.org/10.34920/2020.3.45-48