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The recursive least squares identification algorithm for a class of Wiener nonlinear systems. (English) Zbl 1336.93144

Summary: Many physical systems can be modeled by a Wiener nonlinear model, which consists of a linear dynamic system followed by a nonlinear static function. This work is concerned with the identification of Wiener systems whose output nonlinear function is assumed to be continuous and invertible. A recursive least squares algorithm is presented based on the auxiliary model identification idea. To solve the difficulty of the information vector including the unmeasurable variables, the unknown terms in the information vector are replaced with their estimates, which are computed through the preceding parameter estimates. Finally, an example is given to support the proposed method.

MSC:

93E03 Stochastic systems in control theory (general)
93E24 Least squares and related methods for stochastic control systems
93C10 Nonlinear systems in control theory
93E12 Identification in stochastic control theory
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[1] Shi, Y.; Fang, H., Kalman filter based identification for systems with randomly missing measurements in a network environment, Int. J. Control, 83, 3, 538-551 (2010) · Zbl 1222.93228
[2] Shi, Y.; Yu, B., Output feedback stabilization of networked control systems with random delays modeled by Markov chains, IEEE Trans. Autom. Control, 54, 7, 1668-1674 (2009) · Zbl 1367.93538
[3] Shi, Y.; Yu, B., Robust mixed H-2/H-infinity control of networked control systems with random time delays in both forward and backward communication links, Automatica, 47, 4, 754-760 (2011) · Zbl 1215.93045
[4] Ding, F., System Identification—New Theory and Methods (2013), Science Press: Science Press Beijing
[5] Ding, F., System Identification—Performances Analysis for Identification Methods (2014), Science Press: Science Press Beijing
[6] Hu, P. P.; Ding, F.; Sheng, J., Auxiliary model based least squares parameter estimation algorithm for feedback nonlinear systems using the hierarchical identification principle, J. Frankl. Inst.—Eng. Appl. Math., 350, 10, 3248-3259 (2013) · Zbl 1293.93789
[7] Luan, X. L.; Shi, P.; Liu, F., Stabilization of networked control systems with random delays, IEEE Trans. Ind. Electron., 58, 9, 4323-4330 (2011)
[8] Luan, X. L.; Zhao, S. Y.; Liu, F., H-infinity control for discrete-time Markov jump systems with uncertain transition probabilities, IEEE Trans. Autom. Control, 58, 6, 1566-1572 (2013) · Zbl 1369.93178
[9] Shi, P.; Luan, X. L.; Liu, F., H-infinity filtering for discrete-time systems with stochastic incomplete measurement and mixed delays, IEEE Trans. Ind. Electron., 59, 6, 2732-2739 (2012)
[10] Ding, F.; Wang, X. H.; Chen, Q. J.; Xiao, Y. S., Recursive least squares parameter estimation for a class of output nonlinear systems based on the model decomposition, Circuits Syst. Signal Process., 35 (2016), 10.1007/s00034-015-0190-6
[11] Wang, D. Q., Hierarchical parameter estimation for a class of MIMO Hammerstein systems based on the reframed models, Appl. Math. Lett., 57, 13-19 (2016) · Zbl 1336.93155
[12] Li, H.; Gao, Y.; Shi, P.; Lam, H. K., Observer-based fault detection for nonlinear systems with sensor fault and limited communication capacity, IEEE Trans. Autom. Control (2016), 10.1109/TAC.2015.2503566 · Zbl 1359.93065
[13] Li, H.; Shi, P.; Yao, D.; Wu, L., Observer-based adaptive sliding mode control of nonlinear Markovian jump systems, Automatica, 64, 133-142 (2016) · Zbl 1329.93126
[14] Wang, Y. J.; Ding, F., Iterative estimation for a nonlinear IIR filter with moving average noise by means of the data filtering technique, IMA J. Math. Control Inf. (2016), 10.1093/imamci/dnv067
[15] Li, J. H., Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration, Appl. Math. Lett., 26, 1, 91-96 (2013) · Zbl 1255.65119
[16] Shafiee, G.; Arefi, M. M.; Jahed-Motlagh, M. R.; Jalali, A. A., Nonlinear predictive control of a polymerization reactor based on piecewise linear Wiener model, Chem. Eng. J., 143, 1-3, 282-292 (2008)
[17] Jin, X.; Huang, B.; Shook, D. S., Multiple model LPV approach to nonlinear process identification with EM algorithm, J. Process Control, 21, 1, 182-193 (2011)
[18] da Silva, M. M.; Wigren, T.; Mendon, T., Nonlinear identification of a minimal neuromuscular blockade model in anesthesia, IEEE Trans. Control Syst. Technol., 20, 1, 181-188 (2012)
[19] Pelckmans, K., MINLIP for the identification of monotone Wiener systems, Automatica, 47, 10, 2298-2305 (2011) · Zbl 1228.93124
[20] Xiong, W. L.; Ma, J. X.; Ding, R. F., An iterative numerical algorithm for modeling a class of Wiener nonlinear systems, Appl. Math. Lett., 26, 4, 487-493 (2013) · Zbl 1261.65068
[21] Vörös, J., Parameter identification of Wiener systems with multisegment piecewise-linear nonlinearities, Syst. Control Lett., 56, 2, 99-105 (2007) · Zbl 1112.93019
[22] Hagenblad, A.; Ljung, L.; Wills, A., Maximum likelihood identification of Wiener models, Automatica, 44, 11, 2697-2705 (2008) · Zbl 1152.93508
[23] Hasanov, A.; Romanov, V. G., An inverse coefficient problem related to elastic-plastic torsion of a circular cross-section bar, Appl. Math. Lett., 26, 5, 533-538 (2013) · Zbl 1335.74023
[24] Bai, E. W., A blind approach to the Hammerstein-Wiener model identification, Automatica, 38, 6, 967-979 (2002) · Zbl 1012.93018
[25] Lacy, S. L.; Berntein, D. S., Identification of FIR Wiener systems with unknown, non-invertible, polynomial non-linearities, Int J. Control, 76, 15, 1500-1507 (2003) · Zbl 1050.93074
[26] Janczak, A., Identification of Nonlinear Systems Using Neural Networks and Polynomial Models (2005), Springer: Springer Berlin, Heidelberg · Zbl 1103.93023
[27] Revathy, M. S.; Singh, N. N., An efficient way of solving inverse problem using nonlinear Wiener filter and its application to pattern recognition, Procedia Eng., 38, 708-717 (2012)
[28] Krishtal, I. A.; Okoudjou, K. A., Invertibility of the Gabor frame operator on the Wiener amalgam space, J. Approx. Theory, 153, 2, 212-224 (2008) · Zbl 1283.42045
[29] Hu, Y. B.; Liu, B. L.; Zhou, Q.; Yang, C., Recursive extended least squares parameter estimation for Wiener nonlinear systems with moving average noises, Circuits Syst. Signal Process., 33, 2, 655-664 (2014)
[30] Hu, Y. B.; Liu, B. L.; Zhou, Q., A multi-innovation generalized extended stochastic gradient algorithm for output nonlinear autoregressive moving average systems, Appl. Math. Comput., 247, 218-224 (2014) · Zbl 1343.62059
[31] Ji, Y.; Liu, X. M., New criteria for the robust impulsive synchronization of uncertain chaotic delayed nonlinear systems, Nonlinear Dyn., 79, 1, 1-9 (2015) · Zbl 1331.34108
[32] Ji, Y.; Liu, X. M., Unified synchronization criteria for hybrid switching-impulsive dynamical networks, Circuits Syst. Signal Process., 34, 5, 1499-1517 (2015) · Zbl 1341.93003
[33] Ding, J.; Fan, C. X.; Lin, J. X., Auxiliary model based parameter estimation for dual-rate output error systems with colored noise, Appl. Math. Modell., 37, 6, 4051-4058 (2013)
[34] Ding, F.; Liu, X. M.; Gu, Y., An auxiliary model based least squares algorithm for a dual-rate state space system with time-delay using the data filtering, J. Frankl. Inst., 353, 2, 398-408 (2016) · Zbl 1395.93530
[35] Ding, J.; Lin, J. X., Modified subspace identification for periodically non-uniformly sampled systems by using the lifting technique, Circuits Syst. Signal Process., 33, 5, 1439-1449 (2014)
[36] Wang, X. H.; Ding, F., Convergence of the recursive identification algorithms for multivariate pseudo-linear regressive systems, Int. J. Adapt. Control Signal Process, 30 (2016), 10.1002/acs.2642
[37] Ding, F.; Wang, Y. J.; Ding, J., Recursive least squares parameter identification for systems with colored noise using the filtering technique and the auxiliary model, Digital Signal Process, 37, 100-108 (2015)
[38] Wang, X. H.; Ding, F., Modelling and multi-innovation parameter identification for Hammerstein nonlinear state space systems using the filtering technique, Math. Comput. Model. Dyn. Syst., 22 (2016), http://dx.doi.org/10.1080/13873954.2016.1142455 · Zbl 1339.93106
[39] Wang, Y. J.; Ding, F., Recursive least squares algorithm and gradient algorithm for Hammerstein-Wiener systems using the data filtering, Nonlinear Dyn (2016), 10.1007/s11071-015-2548-5 · Zbl 1354.93158
[40] Wang, Y. J.; Ding, F., Recursive parameter estimation algorithms and convergence for a class of nonlinear systems with colored noise, Circuits Syst. Signal Process, 35 (2016), 10.1007/s00034-015-0210-6 · Zbl 1346.93369
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