IEEE/CAA Journal of Automatica Sinica
Citation:  Y. Hu, C. Zhang, B. Wang, J. Zhao, X. Gong, J. Gao, and H. Chen, “Noisetolerant ZNNBased datadriven iterative learning control for discrete nonaffine nonlinear MIMO repetitive systems,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 2, pp. 344–361, Feb. 2024. doi: 10.1109/JAS.2023.123603 
Aiming at the tracking problem of a class of discrete nonaffine nonlinear multiinput multioutput (MIMO) repetitive systems subjected to separable and nonseparable disturbances, a novel datadriven iterative learning control (ILC) scheme based on the zeroing neural networks (ZNNs) is proposed. First, the equivalent dynamic linearization data model is obtained by means of dynamic linearization technology, which exists theoretically in the iteration domain. Then, the iterative extended state observer (IESO) is developed to estimate the disturbance and the coupling between systems, and the decoupled dynamic linearization model is obtained for the purpose of controller synthesis. To solve the zeroseeking tracking problem with inherent tolerance of noise, an ILC based on noisetolerant modified ZNN is proposed. The strict assumptions imposed on the initialization conditions of each iteration in the existing ILC methods can be absolutely removed with our method. In addition, theoretical analysis indicates that the modified ZNN can converge to the exact solution of the zeroseeking tracking problem. Finally, a generalized example and an applicationoriented example are presented to verify the effectiveness and superiority of the proposed process.
[1] 
C. Hu, R. Zhou, Z. Wang, Y. Zhu, and M. Tomizuka, “Realtime iterative compensation framework for precision mechatronic motion control systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 7, pp. 1218–1232, Jul. 2022. doi: 10.1109/JAS.2022.105689

[2] 
S. R. Nekoo, J. Á. Acosta, G. Heredia, and A. Ollero, “A PDtype statedependent Riccati equation with iterative learning augmentation for mechanical systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 8, pp. 1499–1511, Aug. 2022. doi: 10.1109/JAS.2022.105533

[3] 
D. Huang, C. Chen, T. Huang, D. Zhao, and Q. Tang, “An active repetitive learning control method for lateral suspension systems of highspeed trains,” IEEE Trans. Neural Netw. Learn. Syst., vol. 31, no. 10, pp. 4094–4103, Oct. 2020. doi: 10.1109/TNNLS.2019.2952175

[4] 
Y. Yu, C. Zhang, W. Cao, X. Huang, X. Zhang, and M. Zhou, “Neural network based iterative learning control for magnetic shape memory alloy actuator with iterationdependent uncertainties,” Mech. Syst. Signal Process., vol. 187, p. 109950, Mar. 2023. doi: 10.1016/j.ymssp.2022.109950

[5] 
D. Meng and J. Zhang, “Robust optimizationbased iterative learning control for nonlinear systems with nonrepetitive uncertainties,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 5, pp. 1001–1014, May 2021. doi: 10.1109/JAS.2021.1003973

[6] 
R. Chi, H. Li, N. Lin, and B. Huang, “Datadriven indirect iterative learning control,” IEEE Trans. Cybern., 2023. DOI: 10.1109/TCYB.2022.3232136

[7] 
Q. Wei, L. Zhu, R. Song, P. Zhang, D. Liu, and J. Xiao, “Modelfree adaptive optimal control for unknown nonlinear multiplayer nonzerosum game,” IEEE Trans. Neural Netw. Learn. Syst., vol. 33, no. 2, pp. 879–892, Feb. 2022. doi: 10.1109/TNNLS.2020.3030127

[8] 
Q. Wei, T. Li, and D. Liu, “Learning control for air conditioning systems via human expressions,” IEEE Trans. Ind. Electron., vol. 68, no. 8, pp. 7662–7671, Aug. 2021. doi: 10.1109/TIE.2020.3001849

[9] 
B. Zhao, D. Liu, and C. Luo, “Reinforcement learningbased optimal stabilization for unknown nonlinear systems subject to inputs with uncertain constraints,” IEEE Trans. Neural Netw. Learn. Syst., vol. 31, no. 10, pp. 4330–4340, Oct. 2020. doi: 10.1109/TNNLS.2019.2954983

[10] 
J.X. Xu and Y. Tan, Linear and Nonlinear Iterative Learning Control. Berlin, Germany: Springer, 2003.

[11] 
D. Meng and K. L. Moore, “Contraction mappingbased robust convergence of iterative learning control with uncertain, locally Lipschitz nonlinearity,” IEEE Trans. Syst. Man Cybern. Syst., vol. 50, no. 2, pp. 442–454, Feb. 2020. doi: 10.1109/TSMC.2017.2780131

[12] 
A. Tayebi and C.J. Chien, “A unified adaptive iterative learning control framework for uncertain nonlinear systems,” IEEE Trans. Automat. Control, vol. 52, no. 10, pp. 1907–1913, Oct. 2007. doi: 10.1109/TAC.2007.906215

[13] 
W. He, T. Meng, D. Huang, and X. Li, “Adaptive boundary iterative learning control for an EulerBernoulli beam system with input constraint,” IEEE Trans. Neural Netw. Learn. Syst., vol. 29, no. 5, pp. 1539–1549, May 2018. doi: 10.1109/TNNLS.2017.2673865

[14] 
P. Janssens, G. Pipeleers, and J. Swevers, “A datadriven constrained normoptimal iterative learning control framework for LTI systems,” IEEE Trans. Control Syst. Technol., vol. 21, no. 2, pp. 546–551, Mar. 2013. doi: 10.1109/TCST.2012.2185699

[15] 
H. Sun and A. G. Alleyne, “A computationally efficient norm optimal iterative learning control approach for LTV systems,” Automatica, vol. 50, no. 1, pp. 141–148, Jan. 2014. doi: 10.1016/j.automatica.2013.09.009

[16] 
X. Yu, Z. Hou, and M. M. Polycarpou, “Controllerdynamiclinearizationbased datadriven ILC for nonlinear discretetime systems with RBFNN,” IEEE Trans. Syst. Man Cybern. Syst., vol. 52, no. 8, pp. 4981–4992, Aug. 2022. doi: 10.1109/TSMC.2021.3110790

[17] 
X. Yu, Z. Hou, M. M. Polycarpou, and L. Duan, “Datadriven iterative learning control for nonlinear discretetime MIMO systems,” IEEE Trans. Neural Netw. Learn. Syst., vol. 32, no. 3, pp. 1136–1148, Mar. 2021. doi: 10.1109/TNNLS.2020.2980588

[18] 
Q. Wei and D. Liu, “Datadriven neurooptimal temperature control of watergas shift reaction using stable iterative adaptive dynamic programming,” IEEE Trans. Ind. Electron., vol. 61, no. 11, pp. 6399–6408, Nov. 2014. doi: 10.1109/TIE.2014.2301770

[19] 
H. Lin, B. Zhao, D. Liu, and C. Alippi, “Databased fault tolerant control for affine nonlinear systems through particle swarm optimized neural networks,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 4, pp. 954–964, Jul. 2020. doi: 10.1109/JAS.2020.1003225

[20] 
Y. Yu, C. Zhang, Y. Wang, and M. Zhou, “Neuralnetworkbased iterative learning control for hysteresis in a magnetic shape memory alloy actuator,” IEEE/ASME Trans. Mechatron., vol. 27, no. 2, pp. 928–939, Apr. 2022. doi: 10.1109/TMECH.2021.3075057

[21] 
K. Patan and M. Patan, “Neuralnetworkbased iterative learning control of nonlinear systems,” ISA Trans., vol. 98, pp. 445–453, Mar. 2020. doi: 10.1016/j.isatra.2019.08.044

[22] 
J. Wei, Y. Zhang, and H. Bao, “An exploration on adaptive iterative learning control for a class of commensurate highorder uncertain nonlinear fractional order systems,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 2, pp. 618–627, Mar. 2018. doi: 10.1109/JAS.2017.7510361

[23] 
J. Zhang, B. Cui, X. Dai, and Z. Jiang, “Iterative learning control for distributed parameter systems based on noncollocated sensors and actuators,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 865–871, May 2020. doi: 10.1109/JAS.2019.1911663

[24] 
D. Shen and Y. Xu, “Iterative learning control for discretetime stochastic systems with quantized information,” IEEE/CAA J. Autom. Sinica, vol. 3, no. 1, pp. 59–67, Jan. 2016. doi: 10.1109/JAS.2016.7373763

[25] 
B. Esmaeili, S. S. Madani, M. Salim, M. Baradarannia, and S. Khanmohammadi, “Modelfree adaptive iterative learning integral terminal sliding mode control of exoskeleton robots,” J. Vib. Control, vol. 28, no. 2122, pp. 3120–3139, Nov. 2022. doi: 10.1177/10775463211026031

[26] 
Q. Yu, Z. Hou, X. Bu, and Q. Yu, “RBFNNbased datadriven predictive iterative learning control for nonaffine nonlinear systems,” IEEE Trans. Neural Netw. Learn. Syst., vol. 31, no. 4, pp. 1170–1182, Apr. 2020. doi: 10.1109/TNNLS.2019.2919441

[27] 
Z. Hou, “The parameter identification, adaptive control and model free learning adaptive control for nonlinear system,” Ph.D. dissertation, Northeastern Univ., Shenyang, China, 1994.

[28] 
C. Wang, X. Huo, K. Ma, and R. Ji, “PIDlike model free adaptive control with discrete extended state observer and its application on an unmanned helicopter,” IEEE Trans. Industr. Inform., vol. 19, no. 11, pp. 11265–11274, Nov. 2023. doi: 10.1109/TII.2023.3245223

[29] 
X.Z. Jin, Y.S. Ma, and W.W. Che, “An improved modelfree adaptive control for nonlinear systems: An LMI approach,” Appl. Math. Comput., vol. 447, p. 127910, Jun. 2023.

[30] 
R. Chi, B. Huang, Z. Hou, and S. Jin, “Datadriven highorder terminal iterative learning control with a faster convergence speed,” Int. J. Robust Nonlinear Control, vol. 28, no. 1, pp. 103–119, Jan. 2018. doi: 10.1002/rnc.3861

[31] 
Z. Z. Pan, R. Chi, and Z. Hou, “Compensationbased distributed modelfree adaptive control for cyberattacks,” IEEE Trans. Signal Inf. Process. Netw., vol. 9, pp. 84–94, Feb. 2023.

[32] 
X.Y. Li, “Iterative extended state observer and its application in iterative learning control,” Control Decis., vol. 30, no. 3, pp. 473–478, Mar. 2015.

[33] 
B. Liao, L. Han, X. Cao, S. Li, and J. Li, “Double integralenhanced Zeroing neural network with linear noise rejection for timevarying matrix inverse,” CAAI Trans. Intell. Technol., 2023. DOI: 10.1049/cit2.12161

[34] 
Y. Zhang and S. S. Ge, “Design and analysis of a general recurrent neural network model for timevarying matrix inversion,” IEEE Trans. Neural Netw., vol. 16, no. 6, pp. 1477–1490, Nov. 2005. doi: 10.1109/TNN.2005.857946

[35] 
Z. Sun, G. Wang, L. Jin, C. Cheng, B. Zhang, and J. Yu, “Noisesuppressing zeroing neural network for online solving timevarying matrix square roots problems: A controltheoretic approach,” Expert Syst. Appl., vol. 192, p. 116272, Apr. 2022. doi: 10.1016/j.eswa.2021.116272

[36] 
L. Jia, L. Xiao, J. Dai, Z. Qi, Z. Zhang, and Y. Zhang, “Design and application of an adaptive fuzzy control strategy to zeroing neural network for solving timevariant QP problem,” IEEE Trans. Fuzzy Syst., vol. 29, no. 6, pp. 1544–1555, Jun. 2021. doi: 10.1109/TFUZZ.2020.2981001

[37] 
L. Jin, S. Li, B. Hu, M. Liu, and J. Yu, “A noisesuppressing neural algorithm for solving the timevarying system of linear equations: A controlbased approach,” IEEE Trans. Industr. Inform., vol. 15, no. 1, pp. 236–246, Jan. 2019. doi: 10.1109/TII.2018.2798642

[38] 
Z. Sun, F. Li, B. Zhang, Y. Sun, and L. Jin, “Different modified zeroing neural dynamics with inherent tolerance to noises for timevarying reciprocal problems: A controltheoretic approach,” Neurocomputing, vol. 337, pp. 165–179, Apr. 2019. doi: 10.1016/j.neucom.2019.01.064

[39] 
Z. Hu, L. Xiao, J. Dai, Y. Xu, Q. Zuo, and C. Liu, “A unified predefinedtime convergent and robust ZNN model for constrained quadratic programming,” IEEE Trans. Industr. Inform., vol. 17, no. 3, pp. 1998–2010, Mar. 2021. doi: 10.1109/TII.2020.2996215

[40] 
P. Du, X. Peng, Z. Li, L. Li, and W. Zhong, “Performanceguaranteed adaptive selfhealing control for wastewater treatment processes,” J. Process Control, vol. 116, pp. 147–158, Aug. 2022. doi: 10.1016/j.jprocont.2022.06.004

[41] 
S. Zhao, Q. Yang, P. Cheng, R. Deng, and J. Xia, “Adaptive resilient control for variablespeed wind turbines against false data injection attacks,” IEEE Trans. Sustain. Energy, vol. 13, no. 2, pp. 971–985, Apr. 2022. doi: 10.1109/TSTE.2022.3141766

[42] 
Z. Hou and S. Jin, Model Free Adaptive Control: Theory and Applications. Boca Raton: CRC Press, 2013.

[43] 
X. Zhao, Y. Li, Z. Liu, Q. Li, and W. Chen, “Thermal management system modeling of a watercooled proton exchange membrane fuel cell,” Int. J. Hydrogen Energy, vol. 40, no. 7, pp. 3048–3056, Feb. 2015. doi: 10.1016/j.ijhydene.2014.12.026
