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Nonlinear approximation in control problems. (English) Zbl 0529.93022

MSC:
93B30 System identification
41A20 Approximation by rational functions
93C15 Control/observation systems governed by ordinary differential equations
93B15 Realizations from input-output data
65D10 Numerical smoothing, curve fitting
93C05 Linear systems in control theory
34A55 Inverse problems involving ordinary differential equations
93C99 Model systems in control theory
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References:
[1] N. I. Achiezer: Teorija aproximaciji. GITTL, Moskva 1954.
[2] L. Collatz: Funktionalanalysis und numerische Mathematik. Springer-Verlag, Berlin 1964. · Zbl 0139.09802
[3] P. Eykhoff: System Identification. J. Wiley, London 1974. · Zbl 0667.93102
[4] D. K. Faddeev V. N. Faddeeva: Vyčislitelnyje metody linejnoj algebry. Fizmatgiz, Moskva 1960.
[5] R. Fletcher: Practical Methods of Optimization. Vol. 1: Unconstrained Optimization. J. Wiley, New York 1980. · Zbl 0439.93001
[6] H. O. Hartley: The modified Gauss-Newton for the fitting of nonlinear regression functions by least squares. Technometrics 3 (1961), 269-280. · Zbl 0096.34603
[7] L. V. Kantorovich: O metodě Newtona. Trudy mat. inst. im. Steklova XXVIII, Moskva 1949, 104-144.
[8] D. W. Marquardt: An Algorithm for least-squares estimation of nonlinear parameters. SIAM J. Appl. Math. 11 (1963), 431-441. · Zbl 0112.10505
[9] G. Meinardus: Approximation von Funktionen und ihre numerische Behandlung. Springer-Verlag, Berlin 1964. · Zbl 0124.33103
[10] R. R. Meyer, P. M. Roth: Modified damped least squares. J. Inst. Math. Appl. 9 (1972), 218-233. · Zbl 0243.65003
[11] J. Militký: Řešení úloh regrese. (Solution of the regression problems). Dům techniky, Ostrava 1980.
[12] J. R. Rice: The Approximation of Functions. Addision-Wesley, London 1969. · Zbl 0185.30601
[13] T. Söderström L. Ljung, I. Gustavsson: A theoretical analysis of recursive identification methods. Automatica 14 (1978), 231 - 244. · Zbl 0418.93084
[14] J. Štěpán: Kriterium dominantnosti kořenů. (Criterion of the root dominance). Kybernetika 3 (1967), 1, 58-68.
[15] J. Štěpán: Aproximace funkcí v úlohách regulační techniky. (Approximation of functions in control problems). Kybernetika 3 (1967), 3, 277-292.
[16] J. Štěpán: Some problems of system identification. Kybernetika 7 (1971),2 , 133-155. · Zbl 0223.93038
[17] J. Štěpán: Problémy praktické analýzy složitých systémů. (Some problems of practical analysis of large scale systems). Automatizace 25 (1982), 1, 26-31.
[18] J. Štěpán: A new method for nonlinear approximation of signals. Submitted for publication.
[19] M. A. Wolfe: Numerical Methods for Unconstrained Optimization. Van Nostrand Reinhold, New York 1978. · Zbl 0379.65033
[20] P. Young: Parameter estimation for continuous-time models - A survey. Proceedings of IFAC Congress, Helsinki 1978, Pergamon Press, Oxford 1978.
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