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The strong pointwise convergence of nearest neighbor function fitting algorithm with applications to system identification. (English) Zbl 0579.93062
A nonparametric algorithm for recovering a real-valued function measured with a noise at nonrandomly chosen points of the domain is proposed. The algorithm is based on the k-nearest neighbor rule. Sufficient conditions for strong pointwise convergence are derived. An application of the algorithm to the identification of a step response of a linear dynamical system is presented.
Reviewer: A.Krzyzak

93E12 Identification in stochastic control theory
62G05 Nonparametric estimation
65C99 Probabilistic methods, stochastic differential equations
93C05 Linear systems in control theory
93E25 Computational methods in stochastic control (MSC2010)
Full Text: EuDML
[1] J. Benedetti: On the nonparametric estimation of regression function. J. Roy. Statist. Soc. B39 (1977), 248-253. · Zbl 0367.62088
[2] A. A. Georgiev: Nonparametric system identification by kernel methods. IEEE Trans. Automat. Control AC-29 (1984), 356-358. · Zbl 0532.93064
[3] A. A. Georgiev: A nonparametric algorithm for identification of linear dynamic SISO systems of unknown order. Systems & Control Letters 4 (1984), 273-280. · Zbl 0601.93054
[4] A. A. Georgiev: Nonparametric kernel algorithm for recovery of functions from noisy measurements with applications. IEEE Trans. Automat. Control AC-30 (1985), to appear. · Zbl 0564.93071
[5] G. C. Goodwin, P. L. Payne: Dynamical System Identification: Experiment Design and Data Analysis. Academic Press, New York 1977. · Zbl 0578.93060
[6] W. Greblicki: Nonparametric system identification by orthogonal series. Problems Control Inform. Theory, (1979), 67-73. · Zbl 0407.93057
[7] W. Greblicki: Nearest Neighbor Algorithm for Recovering Functions from Noise. Report No. 30/82/1-6, Technical University of Wroclaw, Wroclaw 1982.
[8] W. Greblicki, A. Krzyżak: Nonparametric identification of a memoryless system with cascade structure. Internal. J. System Sci. 10 (1979), 1301 - 1310. · Zbl 0416.93017
[9] R. L. Kashyap: Maximum likelihood identification of stochastic linear systems. IEEE Trans. Automat. Control AC-15 (1970), 25-34.
[10] M. B. Priestley, M. T. Chao: Nonparametric function fitting. J. Roy. Statist. Soc. B 34 (1972), 385-392. · Zbl 0263.62044
[11] W. E. Pruitt: Summability of independent random variables. J. Math. Mech. 75 (1966), 769-776. · Zbl 0158.36403
[12] E. Rafajłowicz: Nonparametric algorithm for identification of weakly nonlinear static distributed-parameter svstems. Systems & Control Letters 4 (1984), 91 - 96.
[13] L. Rutkowski: On system identification by nonparametric function fitting. IEEE Trans. Automat. Control. AC-27 (1982), 225-227. · Zbl 0471.93065
[14] L. Rutkowski: On nonparametric identification with prediction of time-varying systems. IEEE Trans. Automat. Control AC-29 (1984), 58 - 60. · Zbl 0547.93071
[15] G. N. Saridis Z. J. Nicolic, K. S. Fu: Stochastic approximation for system identification, estimation, and decomposition of mixtures. IEEE Trans. Syst. Sci. Cybern. SSC-5 (1969), 8-15. · Zbl 0184.21801
[16] G. N. Saridis: Expanding subinterval random search for system identification and control. IEEE Trans. Automat. Control. AC-22 (1977), 405-412. · Zbl 0354.93024
[17] E. F. Schuster, S. Yakowitz: Contributions to the theory of nonparametric regression with application to system identification. Ann. Statist. 7 (1979). 139- 149. · Zbl 0401.62033
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