The state-space models are derived for nonuniformly sampled data systems and the corresponding transfer function models are obtained. Since the information vector in the identification model contains unmeasurable true outputs, the conventional stochastic gradient algorithm cannot be applied. In order to overcome this difficulty, the gradient-based iterative identification algorithms are presented by replacing the unmeasurable variables with their iterative estimates at the previous step. The simulation results show that the proposed algorithm has high estimation accuracy compared with the auxiliary model-based stochastic gradient algorithm.
Benchellal, A., Poinot, T., and Trigeassou, J.C. , 2008, ‘‘Fractional modelling and identification of a thermal process,’’ Journal of Vibration and Control14(9-10), 1403-1414.
2.
Ding, F. and Chen, T., 2005a, ‘‘Hierarchical identification of lifted state-space models for general dual-rate systems,’’ IEEE Transactions on Circuits and Systems-I: Regular Papers52(6), 1179-1187.
3.
Ding, F. and Chen, T., 2005b, ‘‘Hierarchical least squares identification methods for multivariable systems,’’ IEEE Transactions on Automatic Control50(3), 397-402.
4.
Ding, F. and Chen, T., 2005c, ‘‘Hierarchical gradient-based identification of multivariable discrete-time systems,’’ Automatica41(2), 315-325.
5.
Ding, F. and Chen, T., 2005d, ‘‘Identification of Hammerstein nonlinear ARMAX systems,’’ Automatica41(9), 1479- 1489.
6.
Ding, F., Chen, T., and Xiao, D.Y., 2004, ‘‘Identification of nonuniformly periodically sampled multirate systems,’’ Acta Electronica Sinica32(9), 1414-1420.
7.
Ding, F., Liu, P.X., and Liu, G., 2009a, ‘‘Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises, ’’ Signal Processing89(10), 1883-1890.
8.
Ding, F., Qiu, L., and Chen, T., 2009b, ‘‘Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems,’’ Automatica45(2), 324-332.
9.
Ding, F., Shi, Y., and Chen, T., 2006a, ‘‘Gradient-based identification methods for Hammerstein nonlinear ARMAX models,’’ Nonlinear Dynamics45(1-2), 31-43.
10.
Ding, F., Shi, Y., and Chen, T., 2006b, ‘‘Performance analysis of estimation algorithms of non-stationary ARMA processes,’’ IEEE Transactions on Signal Processing54(3), 1041-1053.
11.
Garnier, H. and Wang, L., 2008, Identification of Continuous-time Models from Sampled Data, Springer, London.
12.
Han, L.L. and Ding, F., 2009a, ‘‘Multi-innovation stochastic gradient algorithms for multi-input multi-output systems,’’ Digital Signal Processing19(4), 545-554.
13.
Han, L.L. and Ding, F., 2009b, ‘‘Identification for multirate multi-input systems using the multi-innovation identification theory,’’ Computers amp; Mathematics with Applications57(9), 1438- 1449.
14.
Han, L.L., Sheng, J., Ding, F., and Shi, Y., 2009, ‘‘Auxiliary model identification method for multirate multi-input systems based on least squares,’’ Mathematical and Computer Modelling50(7-8), 1100-1106.
15.
Jiang, H.X., Wang, J.H., and Ding, F., 2008, ‘‘Least-squares-iterative identification of a class of non-uniformly sampled-data systems,’’ Systems Engineering and Electrical Technology30(8), 1535-1539.
16.
Lahalle, E., Perez, P.F., and Fleury, G., 2003, ‘‘Simplified LMS algorithms in the case of non-uniformly sampled signals,’’Proceedings of 6th IEEE International Conference on Acoustics, Speech and Signal Processing , Hong Kong, April, Vol. 6, pp. 81-84.
17.
Li, W.H., Shah, S.L., and Xiao, D.Y., 2008, ‘‘Kalman filters in non-uniformly sampled multirate systems: for FDI and beyond,’’ Automatica44(1), 199-208.
18.
Liu, Y.J., Xie, L., and Ding, F., 2009, ‘‘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 Engineering223(4), 445-454.
19.
Qin, P., Lin, Y., and Chen M., 2009, ‘‘Improvement of tracking performance in model-free adaptive controller based on multi-innovation and particle swarm optimization, ’’ International Journal of Innovative Computing, Information and Control5(5), 1367-1377.
20.
Queiroz, M.S.D., 2009, ‘‘An active identification method of rotor unbalance parameters ,’’ Journal of Vibration and Control15(9), 1365-1374.
21.
Silva, S.D., Junior, M.D., and Junior, V.L., 2009, ‘‘Identification of mechanical systems through Kautz filter ,’’ Journal of Vibration and Control15(6), 849-865.
22.
Sheng, J., Chen, T., and Shah, S.L., 2002, ‘‘Generalized predictive control for non-uniformly sampled systems,’’ Journal of Process Control12(8), 875-885.
23.
Schoen, M., 2008, ‘‘Application of genetic algorithms to observer Kalman filter identification,’’ Journal of Vibration and Control14(7), 971-997.
24.
Shi, Y. and Chen, T., 2003, ‘‘Optimal design of multichannel transmultiplexers with stopband energy and passband magnitude constraints,’’ IEEE Transactions on Circuits and Systems II-Analog and Digital Signal Processing50(9), 659- 662.
25.
Shi, Y., Ding, F., and Chen, T., 2006a, ‘‘Multirate crosstalk identification in xDSL systems,’’ IEEE Transactions on Communications54(10), 1878-1886.
26.
Shi, Y., Ding, F., and Chen, T., 2006b, ‘‘2-norm based recursive design of transmultiplexers with designable filter length, Circuits,’’ Systems and Signal Processing25(4), 447-462.
27.
Shi, Y. and Fang, H., 2009, ‘‘Kalman filter based identification for systems with randomly missing measurements in a network environment,’’ International Journal of Control83(3), 538-551.
28.
Shi, Y., Fang, H., and Yan, M., 2009, ‘‘Kalman filter based adaptive control for networked systems with unknown parameters and randomly missing outputs,’’ International Journal of Robust and Nonlinear Control19(18), 1976-1992.
29.
Shi, Y. and Yu, B., 2009, ‘‘Output feedback stabilization of networked control systems with random delays modeled by Markov chains,’’ IEEE Transactions on Automatic Control54(7), 1668-1674.
30.
Wang, D.Q. and Ding, F., 2008, ‘‘Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems,’’ Computers and Mathematics with Applications56(12), 3157-3164.
31.
Xie, L., Ding, J., and Ding, F., 2009, ‘‘Gradient based iterative solutions for general linear matrix equations,’’ Computers and Mathematics with Applications58(7), 1441-1448.
32.
Yu, B., Shi, Y., and Lin, Y., 2009, ‘‘Discrete-time H2 output tracking control of wireless networked control systems with Markov communication models,’’Wireless Communications and Mobile Computing, DOI: 10.1002/wcm.873.
33.
Zhang, J.B., Ding, F., and Shi, Y., 2009, ‘‘Self-tuning control based on multi-innovation stochastic gradient parameter estimation,’’ Systems and Control Letters58(1), 69-75.
34.
Zhu, Y. and Telkamp, H., 2009, ‘‘System identification using slow and irregular output samples,’’ Journal of Process Control19(1), 58-67.
