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Iterative parameter identification methods for nonlinear functions. (English) Zbl 1246.93114
Summary: This paper considers identification problems of nonlinear functions fitting or nonlinear systems modelling. A gradient based iterative algorithm and a Newton iterative algorithm are presented to determine the parameters of a nonlinear system by using the negative gradient search method and Newton method. Furthermore, two model transformation based iterative methods are proposed in order to enhance computational efficiencies. By means of the model transformation, a simpler nonlinear model is achieved to simplify the computation. Finally, the proposed approaches are analyzed using a numerical example.
93E11Filtering in stochastic control
65K05Mathematical programming (numerical methods)
93B30System identification
41A05Interpolation (approximations and expansions)
65H05Single nonlinear equations (numerical methods)
65J22Inverse problems (numerical methods in abstract spaces)
90C90Applications of mathematical programming
[1]Zhang, Y.; Cui, G. M.: Bias compensation methods for stochastic systems with colored noise, Applied mathematical modelling 35, No. 4, 1709-1716 (2011) · Zbl 1217.93163 · doi:10.1016/j.apm.2010.10.003
[2]Zhang, Y.: Unbiased identification of a class of multi-input single-output systems with correlated disturbances using bias compensation methods, Mathematical and computer modelling 53, No. 9-10, 1810-1819 (2011) · Zbl 1219.93141 · doi:10.1016/j.mcm.2010.12.059
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[5]Ding, F.; Chen, T.: On iterative solutions of general coupled matrix equations, SIAM journal on control and optimization 44, No. 6, 2269-2284 (2006) · Zbl 1115.65035 · doi:10.1137/S0363012904441350
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[8]Ding, F.: Transformations between some special matrices, Computers & mathematics with applications 59, No. 8, 2676-2695 (2010) · Zbl 1193.15028 · doi:10.1016/j.camwa.2010.01.036
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[11]Zhang, Z. N.; Ding, F.; Liu, X. G.: Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems, Computers and mathematics with applications 61, No. 3, 672-682 (2011) · Zbl 1217.15022 · doi:10.1016/j.camwa.2010.12.014
[12]Ding, F.; Liu, P. X.; Liu, G. J.: Gradient based and least-squares based iterative identification methods for OE and OEMA systems, Digital signal processing 20, No. 3, 664-677 (2010)
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[38]Ding, F.; Chen, T.: Identification of dual-rate systems based on finite impulse response models, International journal of adaptive control and signal processing 18, No. 7, 589-598 (2004) · Zbl 1055.93018 · doi:10.1002/acs.820
[39]Ding, F.; Chen, T.: Least squares based self-tuning control of dual-rate systems, International journal of adaptive control and signal processing 18, No. 8, 697-714 (2004) · Zbl 1055.93044 · doi:10.1002/acs.828
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[41]Ding, F.; Chen, T.: Parameter estimation of dual-rate stochastic systems by using an output error method, IEEE transactions on automatic control 50, No. 9, 1436-1441 (2005)
[42]Ding, F.; Chen, T.: Hierarchical identification of lifted state-space models for general dual-rate systems, IEEE transactions on circuits and systems – I: Regular papers 52, No. 6, 1179-1187 (2005)
[43]Ding, F.; Chen, T.: A gradient based adaptive control algorithm for dual-rate systems, Asian journal of control 8, No. 4, 314-323 (2006)
[44]Ding, F.; Chen, T.; Iwai, Z.: Adaptive digital control of Hammerstein nonlinear systems with limited output sampling, SIAM journal on control and optimization 45, No. 6, 2257-2276 (2007) · Zbl 1126.93034 · doi:10.1137/05062620X
[45]Ding, F.; Qiu, L.; Chen, T.: Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems, Automatica 45, No. 2, 324-332 (2009) · Zbl 1158.93365 · doi:10.1016/j.automatica.2008.08.007
[46]Liu, Y. J.; Xie, L.; Ding, F.: An auxiliary model based recursive least squares parameter estimation algorithm for non-uniformly sampled multirate systems, Proceedings of the institution of mechanical engineers, part I: Journal of systems and control engineering 223, No. 4, 445-454 (2009)
[47]Shi, Y.; Yu, B.: Output feedback stabilization of networked control systems with random delays modeled by Markov chains, IEEE transactions on automatic control 54, No. 7, 1668-1674 (2009)
[48]Ding, F.; Liu, G.; Liu, X. P.: Partially coupled stochastic gradient identification methods for non-uniformly sampled systems, IEEE transaction on automatic control 55, No. 8, 1976-1981 (2010)
[49]Ding, F.; Ding, J.: Least squares parameter estimation with irregularly missing data, International journal of adaptive control and signal processing 24, No. 7, 540-553 (2010) · Zbl 1200.93130 · doi:10.1002/acs.1141
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[51]Shi, Y.; Fang, H.: Kalman filter based identification for systems with randomly missing measurements in a network environment, International journal of control 83, No. 3, 538-551 (2010) · Zbl 1222.93228 · doi:10.1080/00207170903273987