## Least squares based iterative identification for a class of multirate systems.(English)Zbl 1194.93079

Summary: This paper studies modeling and identification problems for multi-input multirate systems with colored noises. The state-space models are derived for the systems with different input updating periods and furthermore the corresponding transfer functions are obtained. To solve the difficulty of identification models with unmeasurable noises terms, the least squares based iterative algorithm is presented by replacing the unmeasurable variables with their iterative estimates. Finally, the simulation results indicate that the proposed iterative algorithm has advantages over the recursive algorithms.

### MSC:

 93C05 Linear systems in control theory 93E24 Least squares and related methods for stochastic control systems
Full Text:

### References:

 [1] Albertos, P.; Salt, J.; Tormero, J., Dual-rate adaptive control, Automatica, 32, 7, 1027-1030, (1996) · Zbl 0850.93478 [2] Bai, E.W.; Li, D., Convergence of the iterative Hammerstein system identification algorithm, Institute of electrical and electronic engineers transactions on automatic control, 49, 11, 1929-1940, (2004) · Zbl 1365.93098 [3] Chen, T.; Qiu, L., $$H_\infty$$ design of general multirate sampled-data control systems, Automatica, 30, 7, 1139-1152, (1994) · Zbl 0806.93038 [4] Ding, F., System identification theory and methods + Matlab simulations, (2010), China Electric Power Press Beijing, (in Chinese) [5] Ding, F.; Chen, T., Least squares based self-tuning control of dual-rate systems, International journal of adaptive control and signal processing, 18, 8, 697-714, (2004) · Zbl 1055.93044 [6] Ding, F.; Chen, T., Combined parameter and output estimation of dual-rate systems using an auxiliary model, Automatica, 40, 10, 1739-1748, (2004) · Zbl 1162.93376 [7] Ding, F.; Chen, T., Identification of dual-rate systems based on finite impulse response models, International journal of adaptive control and signal processing, 18, 7, 589-598, (2004) · Zbl 1055.93018 [8] Ding, F.; Chen, T., Hierachical identification of lifted state-space models for general dual-rate systems, Institute of electrical and electronic engineers transactions on circuits and systems I: regular papers, 52, 6, 1179-1187, (2005) · Zbl 1374.93342 [9] Ding, F.; Chen, T., Parameter estimation of dual-rate stochastic systems by using an output error method, Institute of electrical and electronic engineers transactions on automatic control, 50, 9, 1436-1441, (2005) · Zbl 1365.93480 [10] Ding, F.; Chen, T., Identification of Hammerstein nonlinear ARMAX systems, Automatica, 41, 9, 1479-1489, (2005) · Zbl 1086.93063 [11] Ding, F.; Chen, T., A gradient based adaptive control algorithm for dual-rate systems, Asian journal of control, 8, 4, 314-323, (2006) [12] Ding, F.; Chen, T., Performance analysis of multi-innovation gradient type identification methods, Automatica, 43, 1, 1-14, (2007) · Zbl 1140.93488 [13] Ding, F.; Chen, T.; Iwai, Z., Adaptive digital control of Hammerstein nonlinear systems with limited output sampling, SIAM journal on control and optimization, 45, 6, 2257-2276, (2006) · Zbl 1126.93034 [14] Ding, F.; Liu, P.X.; Liu, G., Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises, Signal processing, 89, 10, 1883-1890, (2009) · Zbl 1178.94137 [15] Ding, F.; Liu, P.X.; Yang, H.Z., Parameter identification and intersample output estimation for dual-rate systems, Institute of electrical and electronic engineers transactions on systems, man, and cybernetics, part A: systems and humans, 38, 4, 966-975, (2008) [16] Ding, F.; Qiu, L.; Chen, T., Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems, Automatica, 45, 2, 324-332, (2009) · Zbl 1158.93365 [17] Embirucu, M.; Fontes, C., Multirate multivariable generalized predictive control and its application to a slurry reactor for ethylene polymerization, Chemical engineering science, 61, 17, 5754-5767, (2006) [18] Han, L.L.; Ding, F., Identification for multirate multi-input systems using the multi-innovation identification theory, Computers & mathematics with applications, 57, 9, 1438-1449, (2009) · Zbl 1186.93076 [19] Han, L.L.; Ding, F., Multi-innovation stochastic gradient algorithms for multi-input multi-output systems, Digital signal processing, 19, 4, 545-554, (2009) [20] Izadi, I.; Zhao, Q.; Chen, T., An $$H$$-infinity approach to fast rate fault detection for multirate sampled-data systems, Journal of process control, 16, 6, 651-658, (2006) [21] Li, W.; Han, Z.; Shah, S.L., Subspace identification for FDI in systems with non-uniformly sampled multirate data, Automatica, 42, 4, 619-627, (2006) · Zbl 1102.93013 [22] Li, D.; Shah, S.L.; Chen, T., Identification of fast-rate models from multirate data, International journal of control, 74, 6, 680-689, (2001) · Zbl 1038.93017 [23] Li, D.; Shah, S.L.; Chen, T.; Qi, K.Z., Application of dual-rate modeling to CCR octane quality inferential control, Institute of electrical and electronic engineers transactions on control systems technoloy, 11, 1, 43-51, (2003) [24] Li, W.; Shah, S.L.; Xiao, D.Y., Kalman filters in non-uniformly sampled multirate systems: for FDI and beyond, Automatica, 44, 1, 199-208, (2008) · Zbl 1138.93056 [25] Liu, X.G.; Qian, J., Modeling, control and optimization of ideal internal thermally coupled distillation columns, Chemical engineering & technology, 23, 3, 235-241, (2000) [26] Lu, W.; Fisher, D.G., Least-squares output estimation with multirate sampling, Institute of electrical and electronic engineers transactions on automatic control, 34, 6, 669-672, (1989) · Zbl 0678.93057 [27] Lu, J., Liu, X. G., & Ding, F. (2009). Least-squares based iterative parameters estimation for two-input multirate sampled-data systems. In 2009 American control conference (pp. 4379-4383). June 10-12. St. Louis, USA. [28] Qiu, L.; Chen, T., Multirate sampled-data systems: all $$H_\infty$$ suboptimal controllers and the minimum entropy controller, Institute of electrical and electronic engineers transactions on automatic control, 44, 3, 537-550, (1999) · Zbl 0958.93031 [29] Rossiter, J.A.; Sheng, J.; Chen, T.; Shah, S.L., Interpretations of and options in dual-rate predictive control, Journal of process control, 15, 2, 135-148, (2005) [30] Shi, J.; Liu, X.G., Melt index prediction by weighted least squares support vector machines, Journal of applied polymer science, 101, 1, 285-289, (2005) [31] Wang, D.Q.; Ding, F., Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems, Computers & mathematics with applications, 56, 12, 3157-3164, (2008) · Zbl 1165.65308 [32] Zhang, C.; Middleton, R.H.; Evans, R.J., An algorithm for multirate sampling adaptive control, Institute of electrical and electronic engineers transactions on automatic control, 34, 7, 792-795, (1989) · Zbl 0687.93053
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.