A hierarchical least squares identification algorithm for Hammerstein nonlinear systems using the key term separation. (English) Zbl 1390.93818
Summary: Mathematical models are basic for designing controller and system identification is the theory and methods for establishing the mathematical models of practical systems. This paper considers the parameter identification for Hammerstein controlled autoregressive systems. Using the key term separation technique to express the system output as a linear combination of the system parameters, the system is decomposed into several subsystems with fewer variables, and then a Hierarchical Least Squares (HLS) algorithm is developed for estimating all parameters involving in the subsystems. The HLS algorithm requires less computation than the recursive least squares algorithm. The computational efficiency comparison and simulation results both confirm the effectiveness of the proposed algorithms.
MSC:
| 93E12 | Identification in stochastic control theory |
| 03E10 | Ordinal and cardinal numbers |
| 93C10 | Nonlinear systems in control theory |
| 93E03 | Stochastic systems in control theory (general) |
Keywords:
mathematical models; hierarchical least squares identification algorithm; Hammerstein nonlinear systemsReferences:
| [1] | Wang, Y.; Zhao, D.; Li, Y.; Ding, S. X., Unbiased minimum variance fault and state estimation for linear discrete time-varying two-dimensional systems, IEEE Trans. Autom. Control, 62, 10, 5463-5469, (2017) · Zbl 1390.93773 |
| [2] | Wang, Y.; Zhang, H.; Wei, S.; Zhou, D.; Huang, B., Control performance assessment for ILC-controlled batch processes in two-dimensional system framework, IEEE Trans. Syst. Man Cybern. Syst., (2018) |
| [3] | Zhang, W.; Zhao, Y.; Sheng, L., Some remarks on stability of stochastic singular systems with state-dependent noise, Automatica, 51, 273-277, (2015) · Zbl 1309.93182 |
| [4] | Zhang, W.; Lin, X.; Chen, B. S., Lasalle-type theorem and its applications to infinite horizon optimal control of discrete-time nonlinear stochastic systems, IEEE Trans. Autom. Control, 62, 1, 250-261, (2017) · Zbl 1359.93544 |
| [5] | Zhang, X.; Xu, L.; Ding, F.; Hayat, T., Combined state and parameter estimation for a bilinear state space system with moving average noise, J. Frankl. Inst., 355, (2018) · Zbl 1395.93174 |
| [6] | Lin, Y.; Zhang, W., Necessary/sufficient conditions for Pareto optimum in cooperative difference game, Optim. Control Appl. Methods, (2018) · Zbl 1407.91030 |
| [7] | Xu, L., Application of the Newton iteration algorithm to the parameter estimation for dynamical systems, J. Comput. Appl. Math., 288, 33-43, (2015) · Zbl 1314.93062 |
| [8] | Xu, L.; Chen, L.; Xiong, W. L., Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration, Nonlinear Dyn., 79, 3, 2155-2163, (2015) |
| [9] | Xu, L., The damping iterative parameter identification method for dynamical systems based on the sine signal measurement, Signal Process., 120, 660-667, (2016) |
| [10] | Ding, F.; Xu, L.; Zhu, Q. M., Performance analysis of the generalised projection identification for time-varying systems, IET Control Theory Appl., 10, 18, 2506-02514, (2016) |
| [11] | Ding, F.; Wang, F. F.; Xu, L.; Hayat, T.; Alsaedi, A., Parameter estimation for pseudo-linear systems using the auxiliary model and the decomposition technique, IET Control Theory Appl., 11, 3, 390-400, (2017) |
| [12] | Xu, L.; Ding, F., Parameter estimation for control systems based on impulse responses, Int. J. Control Autom. Syst., 15, 6, 2471-2479, (2017) |
| [13] | Yin, S.; Liu, L.; Hou, J., A multivariate statistical combination forecasting method for product quality evaluation, Inf. Sci., 355-356, 229-236, (2016) |
| [14] | Li, J. H.; Zheng, W. X.; Gu, J. P.; Hua, L., Parameter estimation algorithms for Hammerstein output error systems using Levenberg-Marquardt optimization method with varying interval measurements, J. Frankl. Inst., 354, 1, 316-331, (2017) · Zbl 1355.93180 |
| [15] | Ding, F.; Meng, D. D.; Dai, J. Y.; Li, Q. S.; Alsaedi, A.; Hayat, T., Least squares based iterative parameter estimation algorithm for stochastic dynamical systems with ARMA noise using the model equivalence, Int. J. Control Autom. Syst., 16, 2, (2018) |
| [16] | Ding, F.; Xu, L.; Guo, L. J.; Alsaadi, F. E.; Hayat, T., Parameter identification for pseudo-linear systems with ARMA noise using the filtering technique, IET Control Theory Appl., 12, (2018) |
| [17] | Ma, P.; Ding, F.; Zhu, Q. M., Decomposition-based recursive least squares identification methods for multivariate pseudolinear systems using the multi-innovation, Int. J. Syst. Sci., 49, 5, 920-928, (2018) · Zbl 1482.93656 |
| [18] | Bai, E. W., A blind approach to the Hammerstein-Wiener model identification, Automatica, 38, 6, 967-979, (2002) · Zbl 1012.93018 |
| [19] | Bai, E. W., Decoupling the linear and nonlinear parts in Hammerstein model identification, Automatica, 40, 4, 671-676, (2004) · Zbl 1168.93328 |
| [20] | Sjöberg, J.; Zhang, Q.; Ljung, L., Nonlinear black-box modeling in system identification: a unified overview, Automatica, 31, 12, 1691-1724, (1995) · Zbl 0846.93018 |
| [21] | Xu, L., A proportional differential control method for a time-delay system using the Taylor expansion approximation, Appl. Math. Comput., 236, 391-399, (2014) · Zbl 1334.93125 |
| [22] | Xu, L.; Ding, F., Iterative parameter estimation for signal models based on measured data, circuits, Syst. Signal Process., 37, (2018) · Zbl 1411.94026 |
| [23] | Xu, L., The parameter estimation algorithms based on the dynamical response measurement data, Adv. Mech. Eng., 9, 11, 1-12, (2017) |
| [24] | Zhao, S.; Huang, B.; Liu, F., Linear optimal unbiased filter for time-variant systems without a priori information on initial condition, IEEE Trans. Autom. Control, 62, 2, 882-887, (2017) · Zbl 1364.93820 |
| [25] | Zhao, S.; Shmaliy, Y. S.; Liu, F., Fast Kalman-like optimal unbiased FIR filtering with applications, IEEE Trans. Signal Process., 64, 9, 2284-2297, (2016) · Zbl 1414.94748 |
| [26] | Zhao, S.; Shmaliy, Y. S.; Liu, F., On the iterative computation of error matrix in unbiased FIR filtering, IEEE Signal Process. Lett., 24, 5, 555-558, (2017) |
| [27] | Vörös, J., Modeling and parameter identification of systems with multi-segment piecewise-linear characteristics, IEEE Trans. Autom. Control, 47, 1, 184-188, (2002) · Zbl 1364.93173 |
| [28] | Vörös, J., Recursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zones, IEEE Trans. Autom. Control, 48, 12, 2203-2206, (2003) · Zbl 1364.93172 |
| [29] | Xu, L.; Ding, F., The parameter estimation algorithms for dynamical response signals based on the multi-innovation theory and the hierarchical principle, IET Signal Process., 11, 2, 228-237, (2017) |
| [30] | Xu, L.; Ding, F.; Gu, Y.; Alsaedi, A.; Hayat, T., A multi-innovation state and parameter estimation algorithm for a state space system with D-step state-delay, Signal Process., 140, 97-103, (2017) |
| [31] | Zhang, X.; Ding, F.; Alsaadi, A.; Hayat, T., Recursive parameter identification of the dynamical models for bilinear state space systems, Nonlinear Dyn., 89, 4, 2415-2429, (2017) · Zbl 1377.93062 |
| [32] | Li, M. H.; Liu, X. M., The gradient based iterative estimation algorithms for bilinear systems with autoregressive noise, Circuits Syst. Signal Process., 36, 11, 4541-4568, (2017) · Zbl 1373.93095 |
| [33] | Li, M. H.; Liu, X. M., The maximum likelihood least squares based iterative estimation algorithm for bilinear systems with autoregressive moving average noise, J. Frankl. Inst., 354, 12, 4861-4881, (2017) · Zbl 1367.93628 |
| [34] | Li, M. H.; Liu, X. M., Least-squares-based iterative and gradient-based iterative estimation algorithms for bilinear systems, Nonlinear Dyn., 89, 1, 197-211, (2017) · Zbl 1374.93098 |
| [35] | Ding, F.; Wang, X. H., Hierarchical stochastic gradient algorithm and its performance analysis for a class of bilinear-in-parameter systems, circuits, Syst. Signal Process., 36, 4, 1393-1405, (2017) · Zbl 1370.93088 |
| [36] | Chen, H. B.; Ding, F., Hierarchical least squares identification for Hammerstein nonlinear controlled autoregressive systems, Circuits Syst Signal Process., 34, 1, 61-75, (2015) · Zbl 1341.93089 |
| [37] | Goodwin, G. C.; Sin, K. S., Adaptive Filtering Prediction and Control, (1984), Prentice Hall, Englewood Cliffs New Jersey · Zbl 0653.93001 |
| [38] | Ljung, L., System Identification: Theory for the User, (1999), Prentice Hall, Englewood Cliffs New Jersey |
| [39] | Golub, G. H.; Van, C. F., Loan, Matrix Computations, (1996), Johns Hopkins University Press Baltimore, MD · Zbl 0865.65009 |
| [40] | Ding, J. L., Recursive and iterative least squares parameter estimation algorithms for multiple-input-output-error systems with autoregressive noise, Circuits Syst. Signal Process., 37, (2018) · Zbl 1418.93279 |
| [41] | Chen, M.; Ding, F.; Xu, L.; Hayat, T.; Alsaedi, A., Iterative identification algorithms for bilinear-in-parameter systems with autoregressive moving average noise, J. Frankl. Inst., 354, 17, 7885-7898, (2017) · Zbl 1380.93271 |
| [42] | Ding, F.; Wang, X. H.; Mao, L.; Xu, L., Joint state and multi-innovation parameter estimation for time-delay linear systems and its convergence based on the Kalman filtering, Digit. Signal Process., 62, 211-223, (2017) |
| [43] | Ding, F.; Wang, Y. J.; Dai, J. Y.; Li, Q. S.; Chen, Q. J., A recursive least squares parameter estimation algorithm for output nonlinear autoregressive systems using the input-output data filtering, J. Frankl. Inst., 354, 15, 6938-6955, (2017) · Zbl 1373.93393 |
| [44] | Liu, F.; Xue, Q. Y.; Yabuta, K., Rough maximal singular integral and maximal operators supported by subvarieties on Triebel-Lizorkin spaces, Nonlinear Anal., 171, 41-72, (2018) · Zbl 1388.42046 |
| [45] | Zhao, N.; Wu, M. H.; Chen, J. J., Android-based mobile educational platform for speech signal processing, Int. J. Electr. Eng. Educ., 54, 1, 3-16, (2017) |
| [46] | Ji, Y.; Ding, F., Multiperiodicity and exponential attractivity of neural networks with mixed delays, Circuits Syst. Signal Process., 36, 6, 2558-2573, (2017) · Zbl 1370.92019 |
| [47] | Li, X. F.; Chu, Y. D.; Leung, A. Y.T.; Zhang, H., Synchronization of uncertain chaotic systems via complete-adaptive-impulsive controls, Chaos Solitons Fractals, 100, 24-30, (2017) · Zbl 1373.93178 |
| [48] | Zhao, N.; Chen, Y.; Liu, R.; Wu, M. H.; Xiong, W., Monitoring strategy for relay incentive mechanism in cooperative communication networks, Comput. Electr. Eng., 60, 14-29, (2017) |
| [49] | Chi, R. H.; Liu, X. H.; Zhang, R. K.; Huu, Z. S.; Huang, B., Constrained data-driven optimal iterative learning control, J. Process Control, 55, 10-29, (2017) |
| [50] | Chi, R. H.; Lin, N.; Zhang, R. K.; Huang, B.; Feng, Y. J., Stochastic high-order internal model-based adaptive TILC with random uncertainties in initial states and desired reference points, Int. J. Adapt. Control Signal Process., 31, 5, 726-741, (2017) · Zbl 1369.93730 |
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.
