REGULAR ALGORITHMS FOR ADAPTIVE IDENTIFICATION OF LINEAR NON-STATIONARY SYSTEMS

Authors

H.Z. Igamberdiyev, Professor, Department of Information Processing Systems and Control, Tashkent State Technical University, Address: 2 Universitetskaya st., 100095, Tashkent city, Republic of Uzbekistan;Follow
H.I. Sotvoldiev, Ferghana branch of Tashkent University of Information Technologies, Address: 185 Mustaqillik st.,150118, Ferghana city, Republic of Uzbekistan.Follow
U.F Mamirov, Professor, Department of Information Processing Systems and Control, Tashkent State Technical University, Address: 2 Universitetskaya st., 100095, Tashkent city, Republic of Uzbekistan, Phone: (90) 900-56-25;Follow

Abstract

The article deals with the formation of regular algorithms for adaptive parametric spline identification of linear non-stationary systems. Analyzed the issues of constructing adaptive identification of continuous linear non-stationary systems with monotonic and sign-constant parameters. In this case, in a non-stationary system, the entire observation interval is in some way divided into sub-intervals. Identification is carried out at each of the parameter constancy intervals, while the parameter matrix is re-evaluated for the next interval. The input data of the system are determined with an error depending on the error of approximating the state of the system by splines and approximating the ratios by numerical integration formulas. To solve systems of linear algebraic equations, projection algorithm was used, which makes it possible to facilitate the control of the accuracy of intermediate calculations. The above computational procedures make it possible to regularize the problem of adaptive parametric spline identification of linear non-stationary systems based on an iterative algorithm and improve the quality indicators of control processes.

First Page

49

Last Page

54

References

1. N.D.Egupov, K.A.Pupkov, Methods of classical and modern theory of automatic control, Textbook in 5 volumes. Moscow: Publishing house of MSTU named after N.E. Bauman, 2004.
2. V.D.Yurkevich, Synthesis of non-linear non-stationary control systems with multi-tempo processes. St. Petersburg: Nauka, 2000.
3. I.V.Miroshnik, V.O.Nikiforov, A.L.Fradkov, Nonlinear and adaptive control of complex dynamic systems, St.Petersburg: Nauka, 2000, 549 p.
4. E.G.Kleiman, “Identification of non-stationary objects”, Avtomat. i telemekh., issue 10, pp. 3–45, 1999.
5. N.N.Karabutov, Adaptive system identification: information synthesis. 2006, 384 p.
6. V.M.Kuntsevich, Control under Uncertainty: Guaranteed Results in Control and Identification Problems. Kiev: Naukova Dumka, 2006, 264 p.
7. N.V.Plotnikova, N.S.Kalistratova, O.N.Malyavkin, “Algorithms for solving the identification problem”, Computer technologies, management, radio electronics. issue 4, Bulletin of SUSU, no. 14, pp. 133-139, 2006.
8. A.A.Stenin, M.M.Tkach, E.Yu.Melkumyan, “Generalized identification algorithm for linear dynamic systems based on spline functions and Walsh functions”, ASAU. no. 20(40), pp. 131-135, 2012.
9. I.G.Burova, Yu.K.Demyanovich, Minimal splines and their applications. St. Petersburg: Publishing House of St. Petersburg. un-ta, 2010, 364 p.
10. I.G.Burova, Approximation by real and complex minimal splines. St. Petersburg: Ed. house of the St. Petersburg state. un-ta, 2013, 141 p.
11. L.I.Konstantinova, V.A.Kochegurov, B.M.Shumilov, “Parametric identification of nonlinear differential equations based on spline schemes exact on polynomials”, Avtomat. i telemekh., issue 5, pp. 53-63, 1997.
12. S.Kaczmarz, “Approximate solution of systems of linear equations”, Internat. J. Control. Vol. 57, no. 6, pp. 1269-1271, 1993.
13. V.P.Ilyin, “On the iteration method of Kaczmarz and its generalizations”, Sib. magazine industry Mat., Vol. 9(3), pp. 39-49, 2006.
14. J.Saad, Iterative Methods for Spars Linear Systems. Boston: EPS, 1996.
15. U.F.Mamirov, Regular synthesis of adaptive control systems for uncertain dynamic objects. Tashkent: “Bilim va intellektual salohiyat”, 2021, 215 p.
16. V.N.Babenko, “Convergence of Kaczmarz's projection algorithm”, Zh. Vychisl. math. and mat. fiz., Vol. 24(10), pp. 1571-1573, 1984.
17. H.Z.Igamberdiyev, U.F.Mamirov, “Sustainable estimation of parameters and covariation of disturbance vectors in uncertain systems”, Chemical Technology, Control and Management. Vol. 2018: Iss. 3, Article 4, pp. 16-19, 2018. DOI: https://doi.org/10.34920/2018.4-5.16-19.
18. N.Yusupbekov, H.Igamberdiev, U.Mamirov, “Algorithms for Robust Stabilization of a Linear Uncertain Dynamic Object Based on an Iterative Algorithm”, In: Kahraman C., Cebi S., Cevik Onar S., Oztaysi B., Tolga A.C., Sari I.U. (eds) Intelligent and Fuzzy Techniques for Emerging Conditions and Digital Transformation. INFUS 2021. Lecture Notes in Networks and Systems, vol 307. Springer, Cham. https://doi.org/10.1007/978-3-030-85626-7_28
19. N.R.Yusupbekov, H.Z.Igamberdiev, U.F.Mamirov, “Stable Algorithms for Adaptive Control and Adaptation of Uncertain Dynamic Objects Based on Reference Models”, CEUR Workshop Proceedings, Vol. 2965, Kolomna, Russia, pp. 296-302, 2021.
20. Ch.Lawson, R.Henson, Numerical solution of problems in the method of least squares, 1986, 232 p.
21. F.R.Gantmacher, J.L.Brenner, Applications of the Theory of Matrices, Courier Corporation, 2005.

Recommended Citation

Igamberdiyev, H.Z.; Sotvoldiev, H.I.; and Mamirov, U.F (2021) "REGULAR ALGORITHMS FOR ADAPTIVE IDENTIFICATION OF LINEAR NON-STATIONARY SYSTEMS," Chemical Technology, Control and Management: Vol. 2021: Iss. 6, Article 8.
DOI: https://doi.org/10.51346/tstu-02.21.6-77-0052