Iterative learning identification and control for dynamic systems described by NARMAX model

Document Type : Research Article


1 دانشجوی دکتری گروه کنترل ، دانشکده برق، دانشگاه تفرش، تفرش، ایران- دانشجوی فرصت تحقیقاتی دانشگاه امیرکبیر

2 دانشیار گروه کنترل، دانشکده برق، دانشگاه تفرش، تفرش، ایران

3 گروه کنترل، دانشکده برق، دانشگاه صنعتی امیرکبیر، تهران، ایران


A new iterative learning controller is proposed for a general unknown discrete timevarying nonlinear non-affine system represented by NARMAX (Nonlinear Autoregressive Moving Average with eXogenous inputs) model. The proposed controller is composed of an iterative learning neural identifier and an iterative learning controller. Iterative learning control and iterative learning identification are integrated in each iteration. A multi-layer neural network is used for identification. Since the system considered in this paper is time-varying, the proposed neural identifier also is timevarying. The weights of the neural identifier are updated at each iteration, so both tracking performance and identification are improved at each iteration simultaneously. The structure of the proposed neural network used for identification system is affine in control input. Then new iterative learning control law based on the neural identifier is proposed and applied to the system. It should be mentioned that the proposed integrated algorithm has a faster, better and more accurate performance when compared with other iterative learning control algorithms proposed for similar systems. Convergence of both the trajectory tracking error and identification error is guaranteed along the iteration domain with repeating the process within a time-limited range. Simulation and comparison results easily approve the effectiveness of the proposed method


dor 20.1001.1.25882953.2019.

[1] S. Arimoto, S. Kawamura, F. Miyazaki, Bettering operation of robots by learning, Journal of Robotic systems, 1(2) (1984) 123-140.
[2] A. Tayebi, S. Abdul, M. Zaremba, Y. Ye, Robust iterative learning control design: application to a robot manipulator, IEEE/ASME Transactions on mechatronics, 13(5) (2008) 608-613.
[3] L. Zhang, S. Liu, Iterative learning control for flexible manipulator using fourier basis function, International Journal of Automation and Computing, 12(6) (2015) 639-647.
[4] W. Hoffmann, K. Peterson, A.G. Stefanopoulou, Iterative learning control for soft landing of electromechanical valve actuator in camless engines, IEEE Transactions on control systems technology, 11(2) (2003) 174-184.
[5] T. Liu, F. Gao, Y. Wang, IMC-based iterative learning control for batch processes with uncertain time delay, Journal of Process Control, 20(2) (2010) 173-180.
[6] J. Chani-Cahuana, P.N. Landin, C. Fager, T. Eriksson, Iterative learning control for RF power amplifier linearization, IEEE Transactions on Microwave Theory and Techniques, 64(9) (2016) 2778-2789.
[7] H.-S. Ahn, Y. Chen, K.L. Moore, Iterative learning control: Brief survey and categorization, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 37(6) (2007) 1099-1121.
[8] J. Han, D. Shen, C.-J. Chien, Terminal Iterative Learning Control for Discrete-Time Nonlinear System Based on Neural Networks, Journal of the Franklin Institute, 355 (2018) 3641–3658.
[9] M. Kim, T.-Y. Kuc, H. Kim, J.S. Lee, Adaptive iterative learning controller with input learning technique for a class of uncertain MIMO nonlinear systems, International Journal of Control, Automation and Systems, 15(1) (2017) 315-328.
[10] A. Madady, An extended PID type iterative learning control, International Journal of Control, Automation and Systems, 11(3) (2013) 470-481.
[11] A. Madady, H.R. Reza‐Alikhani, A guaranteed monotonically convergent iterative learning control, Asian Journal of Control, 14(5) (2012) 1299-1316.
[12] A. Madady, H.-R. Reza-Alikhani, S. Zamiri, Optimal N-Parametric Type Iterative Learning Control, International Journal of Control, Automation and Systems, 16(5) (2018) 2187-2202.
[13] K. Wan, X.-D. Li, Iterative learning control for two-dimensional linear discrete systems with Fornasini-Marchesini model, International Journal of Control, Automation and Systems, 15(4) (2017) 1710-1719.
[14] J.-X. Xu, Y. Tan, A composite energy function-based learning control approach for nonlinear systems with time-varying parametric uncertainties, IEEE Transactions on Automatic Control, 47(11) (2002) 1940-1945.
[15] S. Yang, J.X. Xu, D. Huang, Y. Tan, Synchronization of heterogeneous multi‐agent systems by adaptive iterative learning control, Asian Journal of Control, 17(6) (2015) 2091-2104.
[16] N. Liu, A. Alleyne, Iterative learning identification for linear time-varying systems, IEEE Transactions on Control Systems Technology, 24(1) (2016) 310-317.
[17] N. Liu, Learning identification and control for repetitive linear time-varying systems, University of Illinois at Urbana-Champaign, 2014.
[18] N. Liu, A. Alleyne, Iterative Learning Identification/Iterative Learning Control for Linear Time-Varying Systems, Journal of Dynamic Systems, Measurement, and Control, 138(10) (2016) 101005.
[19] S. Billings, Identification of nonlinear systems using parameter estimation techniques, in:  Institute of Electrical Engineers Conference, 1981, pp. 183-190.
[20] S. Billings, W. Voon, Least squares parameter estimation algorithms for non-linear systems,  (1984).
[21] S. Chen, S.A. Billings, Representations of non-linear systems: the NARMAX model, International journal of control, 49(3) (1989) 1013-1032.
[22] E. Camporeale, S. Wing, J. Johnson, Machine learning techniques for space weather, Elsevier, 2018.
[23] C.C. Huang, C.H. Loh, Nonlinear identification of dynamic systems using neural networks, Computer‐Aided Civil and Infrastructure Engineering, 16(1) (2001) 28-41.
[24] J. Yan, J.R. Deller Jr, NARMAX model identification using a set-theoretic evolutionary approach, Signal Processing, 123 (2016) 30-41.
[25] X.C. Guan, D.Y. Zhao, Q.M. Zhu, NARMAX modelling and U-model control design for continuous stirred tank reactor (CSTR), in:  2016 35th Chinese Control Conference (CCC), IEEE, 2016, pp. 1964-1969.
[26] M.B. Menhaj, computational intelligence: fundamentals of neural networks, Amir Kabir University Publishing, tehran, iran, (2017) .
[27] M.B. Menhaj, adaptive control systems, Amir Kabir University Publishing, tehran,iran, (2017).
[28] H. Aliyari, S. Hosseinian, H. Sahraei, M. Menhaj, Effect of proximity to high-voltage fields: results of the neural network model and experimental model with macaques, International Journal of Environmental Science and Technology,  (2018) 1-12.
[29] B. Karimi, M.B. Menhaj, Non-affine nonlinear adaptive control of decentralized large-scale systems using neural networks, Information Sciences, 180(17) (2010) 3335-3347.
[30] F. Abedini, M.B. Menhaj, M.R. Keyvanpour, An MLP-based representation of neural tensor networks for the RDF data models, Neural Computing and Applications,  (2017) 1-10.
[31] C.J. Chien, L.C. Fu, An iterative learning control of nonlinear systems using neural network design, Asian Journal of Control, 4(1) (2002) 21-29.
[32] C. Fu, M. Poch, Application of a multi-layered neural network to system identification, International journal of systems science, 24(8) (1993) 1601-1609.
[33] S. Chen, S. Billings, P. Grant, Non-linear system identification using neural networks, International journal of control, 51(6) (1990) 1191-1214.
[34] D. Xu, Z. Li, W. Wu, X. Ding, D. Qu, Convergence of gradient descent algorithm for diagonal recurrent neural networks, in:  2007 Second International Conference on Bio-Inspired Computing: Theories and Applications, IEEE, 2007, pp. 29-31.
[35] D. Xu, H. Zhang, D.P. Mandic, Convergence analysis of an augmented algorithm for fully complex-valued neural networks, Neural Networks, 69 (2015) 44-50.
[36] C. Shao, J. Nie, F. Gao, A Robust Iterative Learning Control with Neural Networks for Robot, IFAC Proceedings Volumes, 37(1) (2004) 779-784.
[37] X. Yu, Z. Hou, C. Yin, Iterative learning control for discrete-time nonlinear systems based on adaptive tuning of 2D learning gain, in:  2017 36th Chinese Control Conference (CCC), IEEE, 2017, pp. 3581-3586.
[38] K. Patan, M. Patan, D. Kowalów, Neural networks in design of iterative learning control for nonlinear systems, IFAC-PapersOnLine, 50(1) (2017) 13402-13407.
[39] K. Patan, M. Patanl, Design and convergence of iterative learning control based on neural networks, in:  2018 European Control Conference (ECC), IEEE, 2018, pp. 1-6.
[40] W.-L. Yan, M.-X. Sun, Identification of discrete-time varying nonlinear systems using time-varying neural networks, in:  2010 8th World Congress on Intelligent Control and Automation, IEEE, 2010, pp. 301-306.
[41] C.-C. Ku, K.Y. Lee, Diagonal recurrent neural networks for dynamic systems control, IEEE transactions on neural networks, 6(1) (1995) 144-156.
[42] C.-H. Lee, C.-C. Teng, Identification and control of dynamic systems using recurrent fuzzy neural networks, IEEE Transactions on fuzzy systems, 8(4) (2000) 349-366.
[43] W.T. Miller, P.J. Werbos, R.S. Sutton, Neural networks for control, MIT press, 1995.
[44] Y.C. Wang and C. J. Chien, An output-recurrent-neural-network-based iterative learning control for unknown nonlinear dynamic plants, Journal of control science and engineering, 2012 (2012), 1-9.