##
**Least squares estimation for a class of non-uniformly sampled systems based on the hierarchical identification principle.**
*(English)*
Zbl 1269.93127

Summary: This paper presents a novel hierarchical least squares algorithm for a class of non-uniformly sampled systems. Based on the hierarchical identification principle, the identification model with a high dimensional parameter vector is decomposed into a group of submodels with lower dimensional parameter vectors. By using the least squares method to identify the submodels and taking a coordinated measure to address the associated items between the submodels, all the system parameters can be estimated. The proposed algorithm can save the computation cost. The performance analysis indicates that parameter estimates converge to their true values. The simulation tests confirm the convergence results.

### MSC:

93E12 | Identification in stochastic control theory |

93C57 | Sampled-data control/observation systems |

93E24 | Least squares and related methods for stochastic control systems |

### Keywords:

hierarchical identification; parameter estimation; non-uniformly sampling; multirate systems; state-space models; least squares estimation
PDFBibTeX
XMLCite

\textit{Y. Liu} et al., Circuits Syst. Signal Process. 31, No. 6, 1985--2000 (2012; Zbl 1269.93127)

Full Text:
DOI

### References:

[1] | A. Al-Smadi, A least-squares-based algorithm for identification of non-Gaussian ARMA models. Circuits Syst. Signal Process. 26(5), 715–731 (2007) · Zbl 1127.62072 |

[2] | T. Chen, B. Francis, Optimal Sampled-Data Control Systems (Springer, London, 1995) · Zbl 0847.93040 |

[3] | M. Cimino, P.R. Pagilla, Design of linear time-invariant controllers for multirate systems. Automatica 46(8), 1315–1319 (2010) · Zbl 1205.93103 |

[4] | M. Cimino, P.R. Pagilla, Conditions for the ripple-free response of multirate systems using linear time-invariant controllers. Syst. Control Lett. 59(8), 510–516 (2010) · Zbl 1198.93122 |

[5] | F. Ding, T. Chen, Hierarchical least squares identification methods for multivariable systems. IEEE Trans. Autom. Control 50(3), 397–402 (2005) · Zbl 1365.93551 |

[6] | F. Ding, T. Chen, Hierarchical identification of lifted state-space models for general dual-rate systems. IEEE Trans. Circuits Syst. I, Regul. Pap. 52(6), 1179–1187 (2005) · Zbl 1374.93342 |

[7] | F. Ding, J. Yang, Hierarchical identification of large scale systems. Acta Autom. Sin. 25(5), 647–654 (1999) |

[8] | F. Ding, L. Qiu, T. Chen, Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems. Automatica 45(2), 324–332 (2009) · Zbl 1158.93365 |

[9] | F. Ding, G. Liu, X.P. Liu, Partially coupled stochastic gradient identification methods for non-uniformly sampled systems. IEEE Trans. Autom. Control 55(8), 1976–1981 (2010) · Zbl 1368.93121 |

[10] | F. Ding, G. Liu, X.P. Liu, Parameter estimation with scarce measurements. Automatica 47(8), 1646–1655 (2011) · Zbl 1232.62043 |

[11] | J. Ding, F. Ding, X.P. Liu, G. Liu, Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data. IEEE Trans. Autom. Control 56(11), 2677–2683 (2011) · Zbl 1368.93744 |

[12] | F. Ding, Y.J. Liu, B. Bao, Gradient based and least squares based iterative estimation algorithms for multi-input multi-output systems. Proc. Inst. Mech. Eng., Part I, J. Syst. Control Eng. 226(1), 43–55 (2012) |

[13] | M. Embiruçu, C. Fontes, Multirate multivariable generalized predictive control and its application to a slurry reactor for ethylene polymerization. Chem. Eng. Sci. 61(17), 5754–5767 (2006) |

[14] | J. Feng, Z. Wang, M. Zeng, Recursive robust filtering with finite-step correlated process noises and missing measurements. Circuits Syst. Signal Process. 30(6), 1355–1368 (2011) · Zbl 1238.93108 |

[15] | H. Fujimoto, Y. Hori, High-performance servo systems based on multirate sampling control. Control Eng. Pract. 10(7), 773–781 (2002) |

[16] | G.C. Goodwin, K.S. Sin, Adaptive Filtering Prediction and Control (Prentice-Hall, Englewood Cliffs, 1984) · Zbl 0653.93001 |

[17] | R.B. Gopaluni, A particle filter approach to identification of nonlinear processes under missing observations. Can. J. Chem. Eng. 86(6), 1081–1092 (2008) |

[18] | S.C. Kadu, M. Bhushan, R. Gudi, Optimal sensor network design for multirate systems. J. Process Control 18(6), 594–609 (2008) |

[19] | H. Li, Y. Shi, Robust H filtering for nonlinear stochastic systems with uncertainties and random delays modeled by Markov chains. Automatica 48(1), 159–166 (2012) · Zbl 1244.93158 |

[20] | D. Li, S.L. Shah, T. Chen, K.Z. Qi, Application of dual-rate modeling to CCR octane quality inferential control. IEEE Trans. Control Syst. Technol. 11(1), 43–51 (2003) |

[21] | W. Li, S.L. Shah, D. Xiao, Kalman filters in non-uniformly sampled multirate systems: for FDI and beyond. Automatica 44(1), 199–208 (2008) · Zbl 1138.93056 |

[22] | Y.J. Liu, F. Ding, Decomposition based least squares estimation algorithm for non-uniformly sampled multirate systems, in Proceedings of the 48th IEEE Conference on Decision and Control, 2009 Held Jointly with the 2009 28th Chinese Control Conference, CDC/CCC 2009. Shanghai, China (2009) |

[23] | X. Liu, J. Lu, Least squares based iterative identification for a class of multirate systems. Automatica 46(3), 549–554 (2010) · Zbl 1194.93079 |

[24] | Y.J. Liu, L. Xie, F. Ding, An auxiliary model based on a recursive least-squares parameter estimation algorithm for non-uniformly sampled multirate systems. Proc. Inst. Mech. Eng., Part I, J. Syst. Control Eng. 223(4), 445–454 (2009) |

[25] | Y.J. Liu, L. Yu, F. Ding, Multi-innovation extended stochastic gradient algorithm and its performance analysis. Circuits Syst. Signal Process. 29(4), 649–667 (2010) · Zbl 1196.94026 |

[26] | L. Ljung, System Identification: Theory for the User (Prentice-Hall, Englewood Cliffs, 1999) · Zbl 0949.93509 |

[27] | B. Ni, D. Xiao, Identification of non-uniformly sampled multirate systems with application to process data compression. IET Control Theory Appl. 4(6), 970–984 (2010) |

[28] | J. Sheng, T. Chen, S.L. Shah, Generalized predictive control for non-uniformly sampled systems. J. Process Control 12(8), 875–885 (2002) |

[29] | Y. Shi, T. Chen, Optimal design of multichannel transmultiplexers with stopband energy and passband magnitude constraints. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. 50(9), 659–662 (2004) |

[30] | Y. Shi, B. Yu, Robust mixed H 2/H 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 |

[31] | M. Srinivasarao, S.C. Patwardhan, R.D. Gudi, Nonlinear predictive control of irregularly sampled multirate systems using blackbox observers. J. Process Control 17(1), 17–35 (2007) · Zbl 1223.93055 |

[32] | Y.S. Suh, Stability and stabilization of nonuniform sampling systems. Automatica 44(12), 3222–3226 (2008) · Zbl 1153.93450 |

[33] | A.K. Tanc, A.H. Kayran, Maximum entropy power spectrum estimation for 2-D multirate systems. Circuits Syst. Signal Process. 31(1), 271–281 (2012) · Zbl 1252.94031 |

[34] | D.N. Vizireanu, Generalizations of binary morphological shape decomposition. J. Electron. Imaging 16(1), 1–6 (2007) |

[35] | D.N. Vizireanu, Morphological shape decomposition interframe interpolation method. J. Electron. Imaging 17(1), 1–5 (2008) |

[36] | D.N. Vizireanu, S. Halunga, G. Marghescu, Morphological skeleton decomposition interframe interpolation method. J. Electron. Imaging 19(2), 1–3 (2010) |

[37] | L. Xie, H.Z. Yang, F. Ding, Modeling and identification for non-uniformly periodically sampled-data systems. IET Control Theory Appl. 4(5), 784–794 (2010) |

[38] | H. Yang, Y. Xia, P. Shi, Stabilization of networked control systems with nonuniform random sampling periods. Int. J. Robust Nonlinear Control 21(5), 501–526 (2011) · Zbl 1214.93093 |

[39] | B. Yu, Y. Shi, H. Huang, l 2–l Filtering for multirate systems based on lifted models. Circuits Syst. Signal Process. 27(5), 699–711 (2008) · Zbl 1173.93360 |

[40] | H. Zhang, Y. Shi, A. Saadat Mehr, Robust energy-to-peak filtering for networked systems with time-varying delays and randomly missing data. IET Control Theory Appl. 4(12), 2921–2936 (2010) |

[41] | H. Zhang, Y. Shi, A. Saadat Mehr, Robust weighted H filtering for networked systems with intermitted measurements of multiple sensors. Int. J. Adapt. Control Signal Process. 25(4), 313–330 (2011) · Zbl 1214.93112 |

[42] | H. Zhang, Y. Shi, A. Saadat Mehr, Robust static output feedback control and remote PID design for networked motor systems. IEEE Trans. Ind. Electron. 58(12), 5396–5405 (2011) |

[43] | H. Zhang, Y. Shi, A. Saadat Mehr, H. Huang, Robust energy-to-peak FIR equalization for time-varying communication channels with intermittent observations. Signal Process. 91(7), 1651–1658 (2011) · Zbl 1213.94054 |

[44] | H. Zhang, Y. Shi, A. Saadat Mehr, Robust H PID control for multivariable networked control systems with disturbance/noise attenuation. Int. J. Robust Nonlinear Control 22(2), 183–204 (2012) · Zbl 1244.93047 |

[45] | Y. Zhu, H. Telkamp, J. Wang, Q. Fu, System identification using slow and irregular output samples. J. Process Control 19(1), 58–67 (2009) · Zbl 1198.93223 |

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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.