×

Parameter identification of ARX models based on modified momentum gradient descent algorithm. (English) Zbl 1441.93319

Summary: The parameter estimation problem of the ARX model is studied in this paper. First, some traditional identification algorithms are briefly introduced, and then a new parameter estimation algorithm – the modified momentum gradient descent algorithm – is developed. Two gradient directions with their corresponding step sizes are derived in each iteration. Compared with the traditional parameter identification algorithms, the modified momentum gradient descent algorithm has a faster convergence rate. A simulation example shows that the proposed algorithm is effective.

MSC:

93E12 Identification in stochastic control theory
93E10 Estimation and detection in stochastic control theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ding, F., Coupled-least-squares identification for multivariable systems, IET Control Theory & Applications, 7, 1, 68-79 (2013) · doi:10.1049/iet-cta.2012.0171
[2] 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 · doi:10.1109/tac.2010.2050713
[3] Ding, F.; Wang, Y.; Ding, J., Recursive least squares parameter identification algorithms for systems with colored noise using the filtering technique and the auxilary model, Digital Signal Processing, 37, 100-108 (2015) · doi:10.1016/j.dsp.2014.10.005
[4] Wang, Y.; Ding, F., Novel data filtering based parameter identification for multiple-input multiple-output systems using the auxiliary model, Automatica, 71, 308-313 (2016) · Zbl 1343.93087 · doi:10.1016/j.automatica.2016.05.024
[5] 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 · doi:10.1109/tac.2011.2158137
[6] Ding, F., Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling, Applied Mathematical Modelling, 37, 4, 1694-1704 (2013) · Zbl 1349.93391 · doi:10.1016/j.apm.2012.04.039
[7] Ding, F., System Identification-Iterative Search Principle and Identification Methods (2018), Beijing, China: Science Press, Beijing, China
[8] Naveros, I.; Ghiaus, C.; Ruíz, D. P.; Castaño, S., Physical parameters identification of walls using ARX models obtained by deduction, Energy and Buildings, 108, 12, 317-329 (2015) · doi:10.1016/j.enbuild.2015.09.021
[9] Qin, Y.; Peng, H.; Zhou, F.; Zeng, X.; Wu, J., Nonlinear modeling and control approach to magnetic levitation ball system using functional weight RBF network-based state-dependent ARX model, Journal of the Franklin Institute, 352, 10, 4309-4338 (2015) · Zbl 1395.93258 · doi:10.1016/j.jfranklin.2015.06.014
[10] Haddouche, R.; Chetate, B.; Boumedine, M. S., Neural network ARX model for gas conditioning tower, International Journal of Modelling and Simulation, 39, 3, 166-177 (2019) · doi:10.1080/02286203.2018.1538848
[11] Na, J.; Yang, Z.; Kamal, S.; Hu, L.; Wang, W.; Zhou, Y., Bio-inspired learning and adaptation for optimization and control of complex systems, Complexity, 2019 (2019) · doi:10.1155/2019/9325364
[12] Na, J.; Li, Y. P.; Huang, Y. B.; Gao, G.; Chen, Q., Output feedback control of uncertain hydraulic servo systems, IEEE Transactions on Industrial Electronics, 67, 1, 490-500 (2019) · doi:10.1109/tie.2019.2897545
[13] Na, J.; Jing, B.; Huang, Y.; Gao, G.; Zhang, C., Unknown system dynamics estimator for motion control of nonlinear robotic systems, IEEE Transactions on Industrial Electronics, 67, 5, 3850-3859 (2020) · doi:10.1109/tie.2019.2920604
[14] Zhu, Q. M., A back propagation algorithm to estimate the parameters of non-linear dynamic rational models, Applied Mathematical Modelling, 27, 3, 169-187 (2003) · Zbl 1033.93064 · doi:10.1016/s0307-904x(02)00097-5
[15] Zhu, Q.; Yu, D.; Zhao, D., An enhanced linear Kalman filter (EnLKF) algorithm for parameter estimation of nonlinear rational models, International Journal of Systems Science, 48, 3, 451-461 (2017) · Zbl 1358.93176 · doi:10.1080/00207721.2016.1186243
[16] Wang, D.; Mao, L.; Ding, F., Recasted models-based hierarchical extended stochastic gradient method for MIMO nonlinear systems, IET Control Theory & Applications, 11, 4, 476-485 (2017) · doi:10.1049/iet-cta.2016.0017
[17] Wang, D.; Zhang, S.; Gan, M.; Qiu, J., A novel EM identification method for Hammerstein systems with missing output data, IEEE Transactions on Industrial Informatics, 16, 4, 2500-2508 (2020) · doi:10.1109/tii.2019.2931792
[18] Zhang, J.; Zhu, Q.; Li, Y., Convergence time calculation for supertwisting algorithm and application for nonaffine nonlinear systems, Complexity, 2019 (2019) · Zbl 1429.93300 · doi:10.1155/2019/6235190
[19] Zhang, J.; Zhu, Q.; Li, Y.; Wu, X. L., Homeomorphism mapping based neural networks for finite time constraint control of a class of nonaffine pure-feedback nonlinear systems, Complexity, 2019 (2019) · Zbl 1417.93053 · doi:10.1155/2019/9053858
[20] Wang, D.; Li, L.; Ji, Y.; Yan, Y., Model recovery for Hammerstein systems using the auxiliary model based orthogonal matching pursuit method, Applied Mathematical Modelling, 54, 537-550 (2018) · Zbl 1480.93431 · doi:10.1016/j.apm.2017.10.005
[21] Ding, F.; Wang, F.; Xu, L.; Hayat, T.; Alsaedi, A., Parameter estimation for pseudo-linear systems using the auxiliary model and the decomposition technique, IET Control Theory & Applications, 11, 3, 390-400 (2017) · doi:10.1049/iet-cta.2016.0491
[22] Ding, F.; Wang, F.; Xu, L.; Wu, M., Decomposition based least squares iterative identification algorithm for multivariate pseudo-linear ARMA systems using the data filtering, Journal of the Franklin Institute, 354, 3, 1321-1339 (2017) · Zbl 1355.93190 · doi:10.1016/j.jfranklin.2016.11.030
[23] Ji, Y.; Jiang, X.; Wan, L., Hierarchical least squares parameter estimation algorithm for two-input Hammerstein finite impulse response systems, Journal of the Franklin Institute, 357, 8, 5019-5032 (2020) · Zbl 1437.93131 · doi:10.1016/j.jfranklin.2020.03.027
[24] Li, M. H.; Liu, X. M., Maximum likelihood least squares based iterative estimation for a class of bilinear systems using the data filtering technique, International Journal of Control Automation and Systems, 18, 6, 1581-1592 (2020) · doi:10.1007/s12555-019-0191-5
[25] Ding, F., Two-stage least squares based iterative estimation algorithm for CARARMA system modeling, Applied Mathematical Modelling, 37, 7, 4798-4808 (2013) · Zbl 1438.93228 · doi:10.1016/j.apm.2012.10.014
[26] Ding, F., Decomposition based fast least squares algorithm for output error systems, Signal Processing, 93, 5, 1235-1242 (2013) · doi:10.1016/j.sigpro.2012.12.013
[27] Jentzen, A.; Wurstemberger, P. V., Lower error bounds for the stochastic gradient descent optimization algorithm: sharp convergence rates for slowly and fast decaying learning rates, Journal of Complexity, 57 (2019) · Zbl 1433.68353 · doi:10.1016/j.jco.2019.101438
[28] Wang, D.; Yan, Y.; Liu, Y.; Ding, J., Model recovery for Hammerstein systems using the hierarchical orthogonal matching pursuit method, Journal of Computational and Applied Mathematics, 345, 135-145 (2019) · Zbl 1398.93349 · doi:10.1016/j.cam.2018.06.016
[29] Ding, F.; Chen, T., Performance analysis of multi-innovation gradient type identification methods, Automatica, 43, 1, 1-14 (2007) · Zbl 1140.93488 · doi:10.1016/j.automatica.2006.07.024
[30] Ding, F.; Liu, X. P.; Liu, G., Multi-innovation least squares identification for linear and pseudo-linear regression models, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 40, 3, 767-778 (2010)
[31] Kyohei, O.; Susumu, F.; Shota, S., Impact of novel incorporation of CT-based segment mapping into a conjugated gradient algorithm on bone SPECT imaging: fundamental characteristics of a context-specific reconstruction method, Asia Oceania Journal of Nuclear Medicine & Biology, 7, 1, 49-57 (2019)
[32] Armstrong, I. S., Spatial dependence of activity concentration recovery for a conjugate gradient (Siemens xSPECT) algorithm using manufacturer-defined reconstruction presets, Nuclear Medicine Communications, 40, 3, 287-293 (2019) · doi:10.1097/mnm.0000000000000960
[33] Heravi, A. R.; Hodtani, G. A., A new correntropy-based conjugate gradient backpropagation algorithm for improving training in neural networks, IEEE Transactions on Neural Networks and Learning Systems, 29, 12, 6252-6263 (2019) · doi:10.1109/tnnls.2018.2827778
[34] Hu, J.; Ma, C., Conjugate gradient least squares algorithm for solving the generalized coupled Sylvester-conjugate matrix equations, Applied Mathematics and Computation, 334, 174-191 (2018) · Zbl 1427.65058 · doi:10.1016/j.amc.2018.03.119
[35] Ding, F.; Liu, Y.; Bao, B., 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, 226, 1, 43-55 (2012) · doi:10.1177/0959651811409491
[36] Ding, F.; Liu, X.; Chu, J., Gradient-based and least-squares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle, IET Control Theory & Applications, 7, 2, 176-184 (2013) · doi:10.1049/iet-cta.2012.0313
[37] Xu, L.; Chen, L.; Xiong, W., Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration, Nonlinear Dynamics, 79, 3, 2155-2163 (2015) · doi:10.1007/s11071-014-1801-7
[38] Xu, L., The damping iterative parameter identification method for dynamical systems based on the sine signal measurement, Signal Processing, 120, 660-667 (2016) · doi:10.1016/j.sigpro.2015.10.009
[39] Xu, L., The parameter estimation algorithms based on the dynamical response measurement data, Advances in Mechanical Engineering, 9, 11 (2017) · doi:10.1177/1687814017730003
[40] Xu, L.; Xiong, W.; Alsaedi, A.; Hayat, T., Hierarchical parameter estimation for the frequency response based on the dynamical window data, International Journal of Control, Automation and Systems, 16, 4, 1756-1764 (2018) · doi:10.1007/s12555-017-0482-7
[41] Ding, F., Combined state and least squares parameter estimation algorithms for dynamic systems, Applied Mathematical Modelling, 38, 1, 403-412 (2014) · Zbl 1449.93254 · doi:10.1016/j.apm.2013.06.007
[42] Zhang, X.; Ding, F., Hierarchical parameter and state estimation for bilinear systems, International Journal of Systems Science, 51, 2, 275-290 (2020) · Zbl 1483.93677 · doi:10.1080/00207721.2019.1704093
[43] Pan, J.; Jiang, X.; Wan, X.; Ding, W., A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems, International Journal of Control, Automation and Systems, 15, 3, 1189-1197 (2017) · doi:10.1007/s12555-016-0081-z
[44] Ma, H.; Pan, J.; Ding, F.; Xu, L.; Ding, W., Partially-coupled least squares based iterative parameter estimation for multi-variable output-error-like autoregressive moving average systems, IET Control Theory & Applications, 13, 18, 3040-3051 (2019) · doi:10.1049/iet-cta.2019.0112
[45] Li, M.; Liu, X.; Ding, F., The filtering-based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle, International Journal of Adaptive Control and Signal Processing, 33, 7, 1189-1211 (2019) · Zbl 1425.93284 · doi:10.1002/acs.3029
[46] Zhang, Y.; Li, X.; Zhao, G.; Lu, B.; Cavalcante, C. C., Signal reconstruction of compressed sensing based on alternating direction method of multipliers, Circuits, Systems, and Signal Processing, 39, 1, 307-323 (2020) · doi:10.1007/s00034-019-01174-2
[47] Pan, J.; Li, W.; Zhang, H., Control algorithms of magnetic suspension systems based on the improved double exponential reaching law of sliding mode control, International Journal of Control, Automation and Systems, 16, 6, 2878-2887 (2018) · doi:10.1007/s12555-017-0616-y
[48] Chang, Y.; Zhai, G.; Fu, B.; Xiong, L., Quadratic stabilization of switched uncertain linear systems: a convex combination approach, IEEE/CAA Journal of Automatica Sinica, 6, 5, 1116-1126 (2019) · doi:10.1109/jas.2019.1911681
[49] Tang, L.; Liu, G. J.; Yang, M.; Li, F.; Ye, F.; Li, C., Joint design and torque feedback experiment of rehabilitation robot, Advances in Mechanical Engineering, 12, 5 (2020) · doi:10.1177/1687814020924498
[50] Wu, T.; Ye, F.; Su, Y.; Wang, Y.; Riffat, S., Coordinated control strategy of DC microgrid with hybrid energy storage system to smooth power output fluctuation, International Journal of Low-Carbon Technologies, 15, 1, 46-54 (2020) · doi:10.1093/ijlct/ctz056
[51] Zhang, Y.; Huang, M.; Wu, T.; Ji, F., Reconfigurable equilibrium circuit with additional power supply, International Journal of Low-Carbon Technologies, 15, 1, 106-111 (2020) · doi:10.1093/ijlct/ctz063
[52] Wang, L.; Liu, H.; Dai, L.; Liu, Y., Novel method for identifying fault location of mixed lines, Energies, 11, 6, 1529 (2018) · doi:10.3390/en11061529
[53] Liu, H.; Zou, Q.; Zhang, Z., Energy disaggregation of appliances consumptions using ham approach, IEEE Access, 7, 185977-185990 (2019) · doi:10.1109/access.2019.2960465
[54] Zhao, N.; Liang, Y.-C.; Pei, Y., Dynamic contract incentive mechanism for cooperative wireless networks, IEEE Transactions on Vehicular Technology, 67, 11, 10970-10982 (2018) · doi:10.1109/tvt.2018.2865951
[55] Zhao, X.; Lin, Z.; Fu, B.; He, L.; Fang, N., Research on automatic generation control with wind power participation based on predictive optimal 2-degree-of-freedom PID strategy for multi-area interconnected power system, Energies, 11, 12, 3325 (2018) · doi:10.3390/en11123325
[56] Ding, F.; Zhang, X.; Xu, L., The innovation algorithms for multivariable state-space models, International Journal of Adaptive Control and Signal Processing, 33, 11, 1601-1618 (2019) · Zbl 1451.93056 · doi:10.1002/acs.3053
[57] Ding, F.; Lv, L.; Pan, J.; Wan, X.; Jin, X.-B., Two-stage gradient-based iterative estimation methods for controlled autoregressive systems using the measurement data, International Journal of Control, Automation and Systems, 18, 4, 886-896 (2020) · doi:10.1007/s12555-019-0140-3
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.