Abstract
We solve the problems of numerical-analytical representation of the solution of an equation describing the dynamic object and its measurable output, as well as optimal computation of the values of continuous linear functionals (numerical characteristics) of measurable functions based on incorrect data containing not only fluctuation error but also singular interference. The method provides the maximum possible decomposition of computational procedures, does not require to carry out traditional linearization operations and the choice of initial approximations, and also is not related to the computation of spectral coefficients in finite linear combinations (with given basic functions) that describe integral curves, measurable functions, and singular interference.
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References
Aleksandrov, A.G., Optimal’nye i adaptivnye sistemy (Optimal and Adaptive Systems), Moscow: Vysshaya Shkola, 1989.
Panteleev, A.V. and Bortakovskii, A.S., Teoriya upravleniya v primerakh i zadachakh (Control Theory in Examples and Problems), Moscow: Vysshaya Shkola, 2003.
Krasovskii, A.A., Theory of Science and Status of the Control Theory, Autom. Remote Control, 2000, vol. 61. no. 4, part 1, pp. 537–553.
Zhdanyuk, B.F., Osnovy statisticheskoi obrabotki traektornykh izmerenii (Fundamentals of Statistical Processing for Trajectory Readings), Moscow: Sovetskoe Radio, 1978.
Bulychev, Yu.G. and Manin, A.P., Matematicheskie aspekty opredeleniya dvizheniya letatel’nykh apparatov (Mathematical Aspects of Motion Identification for Flying Vehicles), Moscow: Mashinostroenie, 2000.
Bulychev, Yu.G., Vasil’ev, V.V., Dzhugan, R.V., et al., Informatsionno-izmeritel’noe obespechenie naturnykh ispytanii slozhnykh tekhnicheskikh kompleksov (Information and Measurement for Live Testing of Complex Technical Systems), Manin, A.P. and Vasil’ev, V.V., Eds., Moscow: Mashinostroenie-Polet, 2016.
Bulychev, Yu.G., Burlai, I.V., and Manin, A.A., Analytic Construction of Control Systems by the Method of Supporting Integral, Autom. Remote Control, 1994, vol. 55, no. 7, part 1, pp. 954–963.
Bulychev, Yu.G. and Manin, A.A., Synthesis of Adaptive Optimal Control Systems for Stochastic Objects from a Forecast Model, Autom. Remote Control, 1995, vol. 56, no. 9, part 2, pp. 1268–1277.
Brandin, V.N., Vasil’ev, A.A., and Khudyakov, S.T., Osnovy eksperimental’noi kosmicheskoi ballistiki (Fundamentals of Experimental Space Ballistics), Moscow: Mashinostroenie, 1974.
Brandin, V.N. and Razorenov, G.N., Opredelenie traektorii kosmicheskikh apparatov (Trajectory Identification for Spacecraft), Moscow: Mashinostroenie, 1978.
Ljung, L., On Model Accuracy in System Identification, Izv. Akad. Nauk, Tekh. Kibern., 1992, no. 6, pp. 55–64.
Vorob’ev, L.M., K teorii poleta raket (On the Theory of Rocket Flight), Moscow: Mashinostroenie, 1970.
Bulychev, Yu.G. and Mel’nikov, A.V., A Numerical-Analytic Method of Studying the Behavior of a Dynamical System Based on Incorrect Observations without Extending the State Space, Zh. Vych. Mat. Mat. Fiz., 2019, vol. 59, no. 6, pp. 937–950.
Leonov, V.A. and Poplavskii, B.K., Filtering of Measurement Errors in the Estimation of Linear Transformations of the Useful Signal, Izv. Akad. Nauk, Tekh. Kibern., 1992, no. 1, pp. 163–170.
Bulychev, Yu.G. and Eliseev, A.V., A Computational Scheme for Invariant-Unbiased Estimation of the Values of Linear Operators from a Given Class, Zh. Vych. Mat. Mat. Fiz., 2008, vol. 48, no. 4, pp. 580–592.
Bulychev, Yu.G., Eliseev, A.V., Borodin, L.I., et al., Generalized Invariant-Unbiased Masking and Estimation of Informational Processes with Multistructural Noise, Autom. Remote Control, 2010, vol. 71, no. 4, pp. 672–680.
Bulychev, Yu.G., Method of Support Integral Curves for solving the Cauchy Problem for Ordinary Differential Equations, Zh. Vych. Mat. Mat. Fiz., 1988, vol. 28, no. 10, pp. 1482–1490.
Bulychev, Yu.G., Methods of Numerical-Analytic Integration of Differential Equations, Zh. Vych. Mat. Mat. Fiz., 1991, vol. 31, no. 9, pp. 1305–1319.
Bibikov, Yu.N., Obshchii kurs obyknovennykh differentsial’nykh uravnenii (A General Course of Ordinary Differential Equations), Leningrad: Leningr. Univ., 1981.
Trenogin, V.A., Funktsional’nyi analiz (Functional Analysis), Moscow: Nauka, 1980.
Tikhonov, A.N., Vasil’eva, A.B., and Sveshnikov, A.G., Differentsial’nye uravneniya (Differential Equations), Moscow: Nauka, 1985.
Kantorovich, L.V. and Akilov, G.P., Funktsional’nyi analiz (Functional Analysis), Moscow: Nauka, 1977.
Babenko, K.I., Osnovy chislennogo analiza (Foundations of Numerical Analysis), Moscow: Nauka, 1986.
Ivanov, V.V., Metody vychislenii na EVM (Methods of Computation on Computers), Kiev: Naukova Dumka, 1986.
Bakhvalov, N.S., Zhidkov, N.P., Kobel’kov, G.M., Chislennye metody (Numerical Methods), Moscow: BINOM. Laboratoriya Znanii, 2008.
Mex-Files, GNU Octave. https://octave.org/doc/interpreter/Mex_002dFiles.html
Techniques to Improve Performance, MATLAB Documentation. https://www.mathworks.com/help/matlab/matlab_prog/techniques-for-improving-performance.html
Acknowledgments
I express my gratitude to my graduate students P.Yu. Radu and A.G. Kondrashov for their help with the computational experiment.
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This paper was recommended for publication by M.M. Khrustalev, a member of the Editorial Board
Russian Text © The Author(s), 2020, published in Avtomatika i Telemekhanika, 2020, No. 6, pp. 131–152.
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Bulychev, Y.G. Some Aspects of Identification of Dynamic Objects under Incorrect Observation Conditions. Autom Remote Control 81, 1073–1090 (2020). https://doi.org/10.1134/S0005117920060090
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DOI: https://doi.org/10.1134/S0005117920060090