Model recovery for Hammerstein systems using the auxiliary model based orthogonal matching pursuit method. (English) Zbl 1480.93431
Summary: This article investigates parameter and order identification of a block-oriented Hammerstein system by using the orthogonal matching pursuit method in the compressive sensing theory which deals with how to recover a sparse signal in a known basis with a linear measurement model and a small set of linear measurements. The idea is to parameterize the Hammerstein system into the linear measurement model containing a measurement matrix with some unknown variables and a sparse parameter vector by using the key variable separation principle, then an auxiliary model based orthogonal matching pursuit algorithm is presented to recover the sparse vector. The standard orthogonal matching pursuit algorithm with a known measurement matrix is a popular recovery strategy by picking the supporting basis and the corresponding non-zero element of a sparse signal in a greedy fashion. In contrast to this, the auxiliary model based orthogonal matching pursuit algorithm has unknown variables in the measurement matrix. For a \(K\)-sparse signal, the standard orthogonal matching pursuit algorithm takes a fixed number of \(K\) stages to pick \(K\) columns (atoms) in the measurement matrix, while the auxiliary model based orthogonal matching pursuit algorithm takes steps larger than \(K\) to pick \(K\) atoms in the measurement matrix with the process of picking and deleting atoms, due to the gradually accurate estimates of the unknown variables step by step. The auxiliary model based orthogonal matching pursuit algorithm can simultaneously identify parameters and orders of the Hammerstein system, and has a high efficient identification performance.
MSC:
| 93E12 | Identification in stochastic control theory |
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
Software:
PDCOReferences:
| [1] | Kim, J.; Konstantinou, K., Digital predistortion of wideband signals based on power amplifier model with memory, Electron. Lett., 37, 23, 1417-1418 (2001) |
| [2] | Jalaleddini, K.; Kearney, R. E., Subspace identification of SISO Hammerstein systems: application to stretch reflex identification, IEEE Trans. Biomed. Eng., 60, 10, 2725-2734 (2013) |
| [3] | Jalaleddini, K.; Tehrani, E. S.; Kearney, R. E., A subspace approach to the structural decomposition and identification of ankle joint dynamic stiffness, IEEE Trans. Biomed. Eng., 64, 6, 1357-1368 (2017) |
| [4] | Butcher, M.; Giustiniani, A.; Masi, A., On the identification of Hammerstein systems in the presence of an input hysteretic nonlinearity with nonlocal memory: piezoelectric actuators-an experimental case study, Phys. B Cond. Matter, 486, 101-105 (2016) |
| [5] | Su, C. L.; Ma, J. W., Nonlinear predictive control using fuzzy Hammerstein model and its application to CSTR process, AASRI Procedia, 3, 8-13 (2012) |
| [6] | van der Veen, G.; Wingerden, J. W.van; Verhaegen, M., Global identification of wind turbines using a Hammerstein identification method, IEEE Trans. Control Syst. Technol., 21, 4, 1471-1478 (2013) |
| [7] | Wu, W.; Jhao, D. W., Control of a direct internal reforming molten carbonate fuel cell system using wavelet network-based Hammerstein models, J. Process Control, 22, 3, 653-658 (2012) |
| [8] | Mao, Y. W.; Ding, F., A novel parameter separation based identification algorithm for Hammerstein systems, Appl. Math. Lett., 60, 21-27 (2016) · Zbl 1339.93109 |
| [9] | Salhi, H.; Kamoun, S., A recursive parametric estimation algorithm of multivariable nonlinear systems described by Hammerstein mathematical models, Appl. Math. Model., 39, 16, 4951-4962 (2015) · Zbl 1443.93016 |
| [10] | Jafari, M.; Salimifard, M.; Dehghani, M., Identification of multivariable nonlinear systems in the presence of colored noises using iterative hierarchical least squares algorithm, ISA Trans., 53, 4, 1243-1252 (2014) |
| [11] | Chen, J.; Liu, Y. J.; Wang, X. H., Recursive least squares algorithm for nonlinear dual-rate systems using missing-output estimation model, circuits, Syst. Signal Process., 36, 4, 1406-1425 (2017) · Zbl 1370.93331 |
| [12] | Bai, E. W.; Li, K., Convergence of the iterative algorithm for a general Hammerstein system identification, Automatica, 46, 11, 1891-1896 (2010) · Zbl 1218.93105 |
| [13] | Li, G. Q.; Wen, C. Y.; Zheng, W. X.; Zhao, G. S., Iterative identification of block-oriented nonlinear systems based on biconvex optimization, Syst. Control Lett., 79, 68-75 (2015) · Zbl 1326.93030 |
| [14] | Ding, F.; Wang, F. F.; Xu, L.; Wu, M. H., Decomposition based least squares iterative identification algorithm for multivariate pseudo-linear ARMA systems using the data filtering, J. Frankl. Inst. Eng. Appl. Math., 354, 3, 1321-1339 (2017) · Zbl 1355.93190 |
| [15] | Ma, J. X.; Ding, F.; Yang, E. F., Data filtering-based least squares iterative algorithm for Hammerstein nonlinear systems by using the model decomposition, Nonlinear Dyn., 83, 4, 1895-1908 (2016) · Zbl 1353.93035 |
| [16] | Vörös, J., Identification of nonlinear cascade systems with output hysteresis based on the key term separation principle, Appl. Math. Model., 39, 18, 5531-5539 (2015) · Zbl 1443.93020 |
| [17] | Vörös, J., Iterative identification of nonlinear dynamic systems with output backlash using three-block cascade models, Nonlinear Dyn., 79, 3, 2187-2195 (2015) |
| [18] | Wang, D. Q.; Liu, H. B.; Ding, F., Highly efficient identification methods for dual-rate Hammerstein systems, IEEE Trans. Control Syst. Technol., 23, 5, 1952-1960 (2015) |
| [19] | Wang, D. Q.; Ding, F.; Chu, Y. Y., Data filtering based recursive least squares algorithm for Hammerstein systems using the key-term separation principle, Inf. Sci., 222, 203-212 (2013) · Zbl 1293.93758 |
| [20] | Wang, D. Q.; Mao, L.; Ding, F., Recasted models based hierarchical extended stochastic gradient method for MIMO nonlinear systems, IET Control Theory Appl., 11, 4, 476-485 (2017) |
| [21] | Xu, L.; Ding, F., 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) |
| [22] | Shen, B. B.; Ding, F.; Alsaedi, A.; Hayat, T., Gradient-based recursive identification methods for input nonlinear equation error closed-loop systems, Circ. Syst. Signal Process., 36, 5, 2166-2183 (2017) · Zbl 1370.93298 |
| [23] | Ding, F.; Wang, X. H., Hierarchical stochastic gradient algorithm and its performance analysis for a class of bilinear-in-parameter systems, Circ. Syst. Signal Process., 36, 4, 1393-1405 (2017) · Zbl 1370.93088 |
| [24] | Wang, D. Q.; Zhang, W., Improved least squares identification algorithm for multivariable Hammerstein systems, J. Frankl. Inst. Eng. Appl. Math., 352, 11, 5292-5307 (2015) · Zbl 1395.93287 |
| [25] | Wang, D. Q.; Zhang, Z.; Yuan, J. Y., Maximum likelihood estimation method for dual-rate Hammerstein systems, Int. J. Control Autom. Syst., 15, 2, 698-705 (2017) |
| [26] | Ma, L.; Liu, X. G., Recursive maximum likelihood method for the identification of Hammerstein ARMAX system, Appl. Math. Model., 40, 13-14, 6523-6535 (2016) · Zbl 1465.93222 |
| [27] | Chen, F. Y.; Ding, F., The filtering based maximum likelihood recursive least squares estimation for multiple-input single-output systems, Appl. Math. Model., 40, 3, 2106-2118 (2016) · Zbl 1452.62693 |
| [28] | Pal, P. S.; Kar, R.; Mandal, D.; Ghoshal, S. P., An efficient identification approach for stable and unstable nonlinear systems using colliding bodies optimization algorithm, ISA Trans., 59, 85-104 (2015) |
| [29] | Chen, J.; Li, J.; Liu, Y. J.; Ding, F., Gradient iterative algorithm for dual-rate nonlinear systems based on a novel particle filter, J. Frankl. Inst. Eng. Appl. Math., 354, 11, 4425-4437 (2017) · Zbl 1380.93251 |
| [30] | 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. Eng. Appl. Math., 354, 1, 316-331 (2017) · Zbl 1355.93180 |
| [31] | Wang, X. H.; Ding, F., Partially coupled extended stochastic gradient algorithm for nonlinear multivariable output error moving average systems, Eng. Comput., 34, 2, 629-647 (2017) |
| [32] | Schnass, K.; Vandergheynst, P., Average performance analysis for thresholding, IEEE Signal Process. Lett., 14, 11, 828-831 (2007) |
| [33] | Hansen, B. E., Sample splitting and threshold estimation, Econometrica, 68, 3, 575-603 (2000) · Zbl 1056.62528 |
| [34] | Blumensath, T.; Davies, M. E., Iterative thresholding for sparse approximations, J. Fourier Anal. Appl., 14, 5, 629-654 (2008) · Zbl 1175.94060 |
| [35] | Mallat, S. G.; Zhang, Z., Matching pursuits with time-frequency dictionaries, IEEE Trans. Signal Process., 41, 12, 3397-3415 (1993) · Zbl 0842.94004 |
| [36] | Tropp, J.; Gilbert, A., Signal recovery from random measurements via orthogonal matching pursuit, IEEE Trans. Inf. Theory, 53, 12, 4655-4666 (2007) · Zbl 1288.94022 |
| [37] | Liu, Y. J.; Tao, T. Y., A CS recovery algorithm for model and time delay identification of MISO-FIR systems, Algorithms, 8, 2, 743-753 (2015) · Zbl 1461.93521 |
| [38] | Chen, S.; Donoho, D.; Saunders, M., Atomic decomposition by basis pursuit, SIAM J. Sci. Comput., 20, 1, 33-61 (1999) · Zbl 0919.94002 |
| [39] | Mota, J. F.C.; Xavier, J.; Aguiar, P. M.Q.; Puschel, M., Distributed basis pursuit, IEEE Trans. Signal Process., 60, 4, 1942-1956 (2012) · Zbl 1391.90478 |
| [40] | Donoho, D.; Elad, M.; Temlyakov, V., Stable recovery of sparse overcomplete representations in the presence of noise, IEEE Trans. Inf. Theory, 52, 1, 6-18 (2006) · Zbl 1288.94017 |
| [41] | Yang, Z.; Zhang, C. S.; Deng, J.; Lu, W. M., Orthonormal expansion \(l_1\) minimization algorithms for compressed sensing, IEEE Trans. Signal Process., 59, 12, 6285-6290 (2011) · Zbl 1393.94724 |
| [42] | Le, V. L.; Lauer, F.; Bloch, G., Selective \(l_1\) minimization for sparse recovery, IEEE Trans. Autom. Control, 59, 11, 3008-3013 (2014) · Zbl 1360.90201 |
| [43] | Mao, Y. W.; Ding, F.; Liu, Y. J., Parameter estimation algorithms for Hammerstein time-delay systems based on the OMP scheme, IET Signal Process., 11, 3, 265-274 (2017) |
| [44] | Villalva, M. G.; Gazoli, J. R.; Filho, E. R., (Modeling and circuit-based simulation of photovoltaic arrays, in: Proceedings of the Power Electronics Conference, COBEP ’09 Brazilian (2009)), 1244-1254 |
| [45] | Villalva, M. G.; Gazoli, J. R.; Filho, E. R., Comprehensive approach to modeling and simulation of photovoltaic arrays, IEEE Trans. Power Electron., 24, 5, 1198-1208 (2007) |
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.
