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Two-stage least squares based iterative identification algorithm for controlled autoregressive moving average (CARMA) systems. (English) Zbl 1247.93018

Summary: A two-stage least squares based iterative (two-stage LSI) identification algorithm is derived for controlled autoregressive moving average (CARMA) systems. The basic idea is to decompose a CARMA system into two subsystems and to identify each subsystem, respectively. Because the dimensions of the involved covariance matrices in each subsystem become small, the proposed algorithm has a high computational efficiency. The simulation results indicate that the proposed algorithm is effective.

MSC:

93E24 Least squares and related methods for stochastic control systems
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F10 Point estimation
65F25 Orthogonalization in numerical linear algebra
93E10 Estimation and detection in stochastic control theory

Software:

CARMA
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[1] Dehghan, M.; Hajarian, M., Matrix equations over (R,S)-symmetric and (R,S)-skew symmetric matrices, Computers & mathematics with applications, 59, 11, 3583-3594, (2010) · Zbl 1202.15017
[2] Dehghan, M.; Hajarian, M., An iterative algorithm for solving a pair of matrix equations AYB\(=\)E, CYD\(=\)F over generalized centro-symmetric matrices, Computers & mathematics with applications, 56, 12, 3246-3260, (2008) · Zbl 1165.15301
[3] Dehghan, M.; Hajarian, M., An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices, Applied mathematical modelling, 34, 3, 639-654, (2010) · Zbl 1185.65054
[4] Dehghan, M.; Hajarian, M., Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation A1X1B1 \(+\) A2X2B2 \(=\) C, Mathematical and computer modelling, 49, 9-10, 1937-1959, (2009) · Zbl 1171.15310
[5] Xie, L.; Ding, J.; Ding, F., Gradient based iterative solutions for general linear matrix equations, Computers & mathematics with applications, 58, 7, 1441-1448, (2009) · Zbl 1189.65083
[6] Ding, J.; Liu, Y.J.; Ding, F., Iterative solutions to matrix equations of form aixbi \(=\) fi, Computers & mathematics with applications, 59, 11, 3500-3507, (2010) · Zbl 1197.15009
[7] Ding, F.; Chen, T., Gradient based iterative algorithms for solving a class of matrix equations, IEEE transactions on automatic control, 50, 8, 1216-1221, (2005) · Zbl 1365.65083
[8] Xie, L.; Ding, J.; Ding, F., Gradient based iterative solutions for general linear matrix equations, Computers and mathematics with applications, 58, 7, 1441-1448, (2009) · Zbl 1189.65083
[9] Wu, A.G.; Li, B.; Yang, Y.; Duan, G.R., Finite iterative solutions to coupled Sylvester-conjugate matrix equations, Applied mathematical modelling, 35, 3, 1065-1080, (2011) · Zbl 1211.15024
[10] Shi, Y.; Fang, H., Kalman filter based identification for systems with randomly missing measurements in a network environment, International journal of control, 83, 3, 538-551, (2010) · Zbl 1222.93228
[11] Shi, Y.; Fang, H.; Yan, M., Kalman filter based adaptive control for networked systems with unknown parameters and randomly missing outputs, International journal of robust and nonlinear control, 19, 18, 1976-1992, (2009), (special issue on control with limited information (part II)) · Zbl 1192.93118
[12] Yu, B.; Shi, Y.; Huang, H., L-2 and \(l\)-infnity filtering for multirate systems using lifted models, Circuits, systems, and signal processing, 27, 5, 699-711, (2008)
[13] Fang, H.; Wu, J.; Shi, Y., Genetic adaptive state estimation with missing input/output data, Proceedings of the institution of mechanical engineers-part I: journal of systems and control engineering, 224, 5, 611-617, (2010)
[14] Shi, Y.; Ding, F.; Chen, T., 2-norm based recursive design of transmultiplexers with designable filter length, Circuits, systems and signal processing, 25, 4, 447-462, (2006) · Zbl 1130.94312
[15] Xiao, Y.S.; Zhang, Y.; Ding, J.; Dai, J.Y., The residual based interactive least squares algorithms and simulation studies, Computers & mathematics with applications, 58, 6, 1190-1197, (2009) · Zbl 1189.62149
[16] Wang, L.Y.; Xie, L.; Wang, X.F., The residual based interactive stochastic gradient algorithms for controlled moving average models, Applied mathematics and computation, 211, 2, 442-449, (2009) · Zbl 1162.93037
[17] Ding, F.; Chen, T.; Qiu, L., Bias compensation based recursive least squares identification algorithm for MISO systems, IEEE transactions on circuits and systems - II: express briefs, 53, 5, 349-353, (2006)
[18] Ding, F.; Shi, Y.; Chen, T., Performance analysis of estimation algorithms of non-stationary ARMA processes, IEEE transactions on signal processing, 54, 3, 1041-1053, (2006) · Zbl 1373.94569
[19] Ding, F.; Liu, P.X.; Liu, G.L., Gradient based and least-squares based iterative identification methods for OE and OEMA systems, Digital signal processing, 20, 3, 664-677, (2010)
[20] Wang, D.Q.; Yang, G.W.; Ding, R.F., Gradient-based iterative parameter estimation for box – jenkins systems, Computers & mathematics with applications, 60, 5, 1200-1208, (2010) · Zbl 1201.94046
[21] Liu, Y.J.; Wang, D.Q.; Ding, F., Least squares based iterative identification for identifying box – jenkins models with finite measurement date, Digital signal processing, 20, 5, 1458-1467, (2010)
[22] Ding, F.; Chen, T., Identification of Hammerstein nonlinear ARMAX systems, Automatica, 41, 9, 1479-1489, (2005) · Zbl 1086.93063
[23] Han, H.Q.; Xie, L.; Ding, F.; Liu, X.G., Hierarchical least-squares based iterative identification for multivariable systems with moving average noises, Automatica, 51, 9-10, 1213-1220, (2010) · Zbl 1198.93216
[24] Zhang, Z.N.; Ding, F.; Liu, X.G., Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems, Computers & mathematics with applications, 61, 3, 672-682, (2011) · Zbl 1217.15022
[25] Bao, B.; Xu, Y.Q.; Sheng, J.; Ding, R.F., Least squares based iterative parameter estimation algorithm for multivariable controlled ARMA system modelling with finite measurement data, Mathematical and computer modelling, 53, 9-10, 1664-1669, (2011) · Zbl 1219.62133
[26] F. Ding, Y.J. Liu, B. Bao, Gradient based and least squares based iterative estimation algorithms for multi-input multi-output systems, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering (2011), in press (doi:10.1177/0959651811409491).
[27] Bai, E.W., An optimal two-stage identification algorithm for hammerstein – wiener nonlinear systems, Automatica, 34, 3, 333-338, (1998) · Zbl 0915.93018
[28] Li, K.; Peng, J.X.; Bai, E., A two-stage algorithm for identification of nonlinear dynamic systems, Automatica, 42, 7, 1189-1197, (2006) · Zbl 1117.93314
[29] Hwang, S.H.; Lai, S.T., Use of two-stage least-squares algorithms for identification of continuous systems with time delay based on pulse responses, Automatica, 40, 9, 1561-1568, (2004) · Zbl 1055.93506
[30] Cao, Z.H., Rounding error analysis of two-stage iterative methods for large linear systems, Applied mathematics and computation, 139, 2-3, 371-381, (2003) · Zbl 1029.65026
[31] Duan, H.H.; Jia, J.; Ding, R.F., Two-stage recursive least squares parameter estimation algorithm for output error models, Mathematical and computer modelling, 55, x, (2012) · Zbl 1255.93133
[32] 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
[33] Chen, J.; Zhang, Y.; Ding, R.F., Auxiliary model based multi-innovation algorithms for multivariable nonlinear systems, Mathematical and computer modelling, 52, 9-10, 1428-1434, (2010) · Zbl 1205.93142
[34] Wang, D.Q., Least squares-based recursive and iterative estimation for output error moving average (OEMA) systems using data filtering, IET control theory and applications, 5, 14, 1648-1657, (2011)
[35] Wang, D.Q.; Ding, F., Input – output data filtering based recursive least squares parameter estimation for CARARMA systems, Digital signal processing, 20, 4, 991-999, (2010)
[36] Han, L.L.; Ding, F., Parameter estimation for multirate multi-input systems using auxiliary model and multi-innovation, Journal of systems engineering and electronics, 21, 6, 1079-1083, (2010)
[37] 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
[38] 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
[39] 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
[40] 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
[41] Ding, F.; Chen, T., Parameter estimation of dual-rate stochastic systems by using an output error method, IEEE transactions on automatic control, 50, 9, 1436-1441, (2005) · Zbl 1365.93480
[42] Liu, Y.J.; Sheng, J.; Ding, R.F., Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems, Computers & mathematics with applications, 59, 8, 2615-2627, (2010) · Zbl 1193.60057
[43] Ding, F.; Chen, T., Performance analysis of multi-innovation gradient type identification methods, Automatica, 43, 1, 1-14, (2007) · Zbl 1140.93488
[44] Liu, Y.J.; Xiao, Y.S.; Zhao, X.L., Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model, Applied mathematics and computation, 215, 4, 1477-1483, (2009) · Zbl 1177.65095
[45] 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
[46] Zhang, J.B.; Ding, F.; Shi, Y., Self-tuning control based on multi-innovation stochastic gradient parameter estimation, Systems & control letters, 58, 1, 69-75, (2009) · Zbl 1154.93040
[47] Ding, F.; Liu, P.X.; Liu, G., Multi-innovation least squares identification for system modeling, IEEE transactions on systems, man, and cybernetics, part B: cybernetics, 40, 3, 767-778, (2010)
[48] Ding, F., Several multi-innovation identification methods, Digital signal processing, 20, 4, 1027-1039, (2010)
[49] Wang, D.Q.; Ding, F., Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems, Digital signal processing, 20, 3, 750-762, (2010)
[50] Xie, L.; Yang, H.Z.; Ding, F., Modeling and identification for non-uniformly periodically sampled-data systems, IET control theory & applications, 4, 5, 784-794, (2010)
[51] Han, L.L.; Ding, F., Multi-innovation stochastic gradient algorithms for multi-input multi-output systems, Digital signal processing, 19, 4, 545-554, (2009)
[52] Liu, Y.J.; Yu, L.; Ding, F., Multi-innovation extended stochastic gradient algorithm and its performance analysis, Circuits, systems and signal processing, 29, 4, 649-667, (2010) · Zbl 1196.94026
[53] Ding, F.; Chen, T., Hierarchical gradient-based identification of multivariable discrete-time systems, Automatica, 41, 2, 315-325, (2005) · Zbl 1073.93012
[54] Ding, F.; Chen, T., Hierarchical least squares identification methods for multivariable systems, IEEE transactions on automatic control, 50, 3, 397-402, (2005) · Zbl 1365.93551
[55] 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, 6, 1179-1187, (2005) · Zbl 1374.93342
[56] Ding, F.; Chen, T., A gradient based adaptive control algorithm for dual-rate systems, Asian journal of control, 8, 4, 314-323, (2006)
[57] 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, (2007) · Zbl 1126.93034
[58] 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
[59] 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, 4, 445-454, (2009)
[60] Ding, F.; Liu, G.; Liu, X.P., Partially coupled stochastic gradient identification methods for non-uniformly sampled systems, IEEE transactions on automatic control, 55, 8, 1976-1981, (2010) · Zbl 1368.93121
[61] Ding, F.; Ding, J., Least squares parameter estimation with irregularly missing data, International journal of adaptive control and signal processing, 24, 7, 540-553, (2010) · Zbl 1200.93130
[62] Ding, F.; Liu, G.; Liu, X.P., Parameter estimation with scarce measurements, Automatica, 47, 8, 1646-1655, (2011) · Zbl 1232.62043
[63] Xie, L.; Yang, H.Z.; Ding, F., Recursive least squares parameter estimation for non-uniformly sampled systems based on the data filtering, Mathematical and computer modelling, 54, 1-2, 315-324, (2011) · Zbl 1225.62120
[64] Chen, J.; Ding, F., Modified stochastic gradient algorithms with fast convergence rates, Journal of vibration and control, 17, 9, 1281-1286, (2011) · Zbl 1271.93043
[65] Ding, J.; Shi, Y.; Wang, H.G.; Ding, F., A modified stochastic gradient based parameter estimation algorithm for dual-rate sampled-data systems, Digital signal processing, 20, 4, 1238-1249, (2010)
[66] Ding, F.; Liu, P.X.; Yang, H.Z., Parameter identification and intersample output estimation for dual-rate systems, IEEE transactions on systems, man, and cybernetics, part A: systems and humans, 38, 4, 966-975, (2008)
[67] Ding, F.; Yang, H.Z.; Liu, F., Performance analysis of stochastic gradient algorithms under weak conditions, Science in China series F: information sciences, 51, 9, 1269-1280, (2008) · Zbl 1145.93050
[68] Ding, F.; Chen, T., Performance bounds of the forgetting factor least squares algorithm for time-varying systems with finite measurement data, IEEE transactions on circuits and systems—I: regular papers, 52, 3, 555-566, (2005) · Zbl 1374.93390
[69] Wang, W.; Ding, F.; Dai, J.Y., Maximum likelihood least squares identification for systems with autoregressive moving average noise, Applied mathematical modelling, 36, x, (2012) · Zbl 1242.62105
[70] Ding, J.; Ding, F.; Liu, X.P.; Liu, G., Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data, IEEE transactions on automatic control, 56, 11, 2677-2683, (2011) · Zbl 1368.93744
[71] Ding, J.; Ding, F., Bias compensation based parameter estimation for output error moving average systems, International journal of adaptive control and signal processing, 25, 12, 1100-1111, (2011) · Zbl 1263.93215
[72] Zhuang, L.F.; Pan, F.; Ding, F., Parameter and state estimation algorithm for single-input single-output linear systems using the canonical state space models, Applied mathematical modelling, 26, x, (2012) · Zbl 1252.93045
[73] Li, J.H.; Ding, F., Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique, Computers & mathematics with applications, 62, 11, 4170-4177, (2011) · Zbl 1236.93150
[74] Ding, F.; Liu, P.X.; Liu, G., Identification methods for Hammerstein nonlinear systems, Digital signal processing, 21, 2, 215-238, (2011)
[75] Wang, D.Q.; Chu, Y.Y.; Ding, F., Auxiliary model-based RELS and MI-ELS algorithms for Hammerstein OEMA systems, Computers & mathematics with applications, 59, 9, 3092-3098, (2010) · Zbl 1193.93170
[76] Wang, D.Q.; Chu, Y.Y.; Yang, G.W.; Ding, F., Auxiliary model-based recursive generalized least squares parameter estimation for Hammerstein OEAR systems, Mathematical and computer modelling, 52, 1-2, 309-317, (2010) · Zbl 1201.93134
[77] Wang, D.Q.; Ding, F., Least squares based and gradient based iterative identification for Wiener nonlinear systems, Signal processing, 91, 5, 1182-1189, (2011) · Zbl 1219.94052
[78] Ding, F.; Shi, Y.; Chen, T., Auxiliary model based least-squares identification methods for Hammerstein output-error systems, Systems & control letters, 56, 5, 373-380, (2007) · Zbl 1130.93055
[79] Ding, F.; Shi, Y.; Chen, T., Gradient-based identification methods for Hammerstein nonlinear ARMAX models, Nonlinear dynamics, 45, 1-2, 31-43, (2006) · Zbl 1134.93321
[80] 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
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