Abstract
The article presents the regularized algorithms for identification of uncertain dynamic management objects. Various algorithms for identifying dynamic control objects are analyzed in the conditions of approximate assignment of source data. Regularization, moderate spoilage, and imaginary shift methods for extended systems are presented. The results of solving various model problems for different error levels of the initial data are shown. It is shown that the best indicators are provided by the simplified regularization method for an extended system of equations, since this extended system is by definition symmetric and positive definite.
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References
Egupov, N.D., Pupkov, K.A.: Methods of classical and modern theory of automatic control. Textbook in 5 volumes. Publishing house of MSTU named after N.E. Bauman, Moscow (2004)
Afanasyev, V.N.: Control of Indefinite Systems. Peoples’ Friendship University of Russia, Moscow (2008)
Bobtsov, A.A., Pyrkin, A.A.: Adaptive and Robust Control with Uncertainty Compensation. ITMO National Research University, St. Petersburg (2013)
Afanasyev, V.N.: Control of Indefinite Dynamic Objects. Fizmat-ref, Moscow (2008)
Nikiforov, V.O., Ushakov, A.V.: Control Under Uncertainty: Sensitivity, Adaptation, Robustness. Gitmo (TU), St. Petersburg (2002)
Igamberdiev, H.Z., Yusupbekov, A.N., Zaripov, O.O.: Regular Methods of Estimation and Control of Dynamic Objects Under Uncertainty. TashSTU, Tashkent (2012)
Igamberdiyev, K., Mamirov, U.F.: Regularized synthesis algorithms of parametrically invariant control systems of uncertain objects. J. Chem. Technol. Control Manage. 5, 62–65 (2016)
Demyanov, V.F., Tamasyan, G.: On direct Methods for solving variational problems. Proc. Inst. Math. Mech. Ural Branch Russ. Acad. Sci. 16(5), 36–47 (2010)
Vasin, V.V., Ageev, A.L.: Ill-Posed Problems with a Priori Information. Nauka, Yekaterinburg (1993)
Tikhonov, A.N., Arsenin, V.Y.: Methods for Solving Ill –Posed Problems. Nauka, Moscow (1986)
Tikhonov, A.N., Goncharsky, A.V.: Incorrect Problems of Natural Science. Publishing house of Moscow state University, Moscow (1987)
Morozov, V.A.: Algorithmic bases of methods for solving incorrect problems. Comput. Methods Program. 45, 130–141 (2003)
Zhdanov, A.I.: Introduction to Methods for Solving Ill-Posed Problems. Aerospace University, Samara (2006)
Yusupbekov, N., Igamberdiev, H., Mamirov, U.: Algorithms of sustainable estimation of unknown input signals in control systems. J. Multiple-Valued Logic Soft Comput. 33(1–2), 1–10 (2019). https://www.oldcitypublishing.com/pdf/9291
Igamberdiev, H.Z., Yusupbekov, A.N., Karimov, D.R., Shukurova, O.P.: Stable algorithms for adaptation of objects with control delay. In: Aliev, R., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F. (eds) 10th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions - ICSCCW-2019. ICSCCW 2019. Advances in Intelligent Systems and Computing, 1095. Springer, Cham (2020). http://webvpn.fjmu.edu.cn/10.1007/978-3-030-35249-3_95
Sevinov, J.U., Zaripov, O.O., Zaripova, S.O.: The algorithm of adaptive estimation in the synthesis of the dynamic objects control systems. Int. J. Adv. Sci. Technol. 29(5), 1096–1100 (2020). http://sersc.org/journals/index.php/IJAST/article/view/7887
Igamberdiev, H.Z., Yusupov, E.A., Sotvoldiev, H.I., Azamxonov, B.S. Sustainable algorithms for the synthesis of a suboptimal dynamic object management system. In: Aliev, R., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F. (eds) 10th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions - ICSCCW-2019. ICSCCW 2019. Advances in Intelligent Systems and Computing, 1095. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_120
Lawson, C.L., Henson, R.J.: Solving Least Squares Problems. Prentice-Hall, New Jersey, Englewood Cliffs, USA (1986)
Godunov, S.K., Antonov, A.G., Kirilyuk, O.P., Kostin, V.I.: Guaranteed Accuracy for Solving Systems of Linear Equations in Euclidean Spaces. Nauka, Novosibirsk (1988)
Igamberdiev, H.Z., Boeva, O.H., Sevinov, J.U.: Sustainable algorithms for selecting feedback in dynamic object management systems. J. Adv. Res. Dyn. Control Syst. 12(7), 2162–2166 (2020). https://doi.org/10.5373/jardcs/v12sp7/20202337
Bakushinsky, A.B., Goncharsky, A.V.: Iterative Methods for Solving Ill - Posed Problems. Nauka, Moscow (1989)
Nazimov, A.B., Morozov, V.A., Mukhamadiev, E.M., Mullojanov, M.: Shift Regularization Method Theory and Applications. VogTU, Vologda (2012)
Igamberdiev, H.Z., Mamirov, U.F.: Regularized algorithms for identification of undefined dynamic control objects. J. Bull. Tashkent State Tech. Univ. 2, 16–21 (2018)
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Igamberdiev, H.Z., Mamirov, U.F. (2021). Regular Algorithms for the Parametric Estimation of the Uncertain Object Control. In: Aliev, R.A., Yusupbekov, N.R., Kacprzyk, J., Pedrycz, W., Sadikoglu, F.M. (eds) 11th World Conference “Intelligent System for Industrial Automation” (WCIS-2020). WCIS 2020. Advances in Intelligent Systems and Computing, vol 1323. Springer, Cham. https://doi.org/10.1007/978-3-030-68004-6_42
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