Data-Driven Learning Control Algorithms for Unachievable Tracking Problems

Zeyi Zhang; Hao Jiang; Dong Shen; Samer S. Saab

doi:10.1109/JAS.2023.123756

Volume 11 Issue 1

Jan. 2024

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2024 > 11(1): 205-218

Z. Zhang, H. Jiang, D. Shen, and S. Saab, “Data-driven learning control algorithms for unachievable tracking problems,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 1, pp. 205–218, Jan. 2024. doi: 10.1109/JAS.2023.123756

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Z. Zhang, H. Jiang, D. Shen, and S. Saab, “Data-driven learning control algorithms for unachievable tracking problems,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 1, pp. 205–218, Jan. 2024. doi: 10.1109/JAS.2023.123756

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Data-Driven Learning Control Algorithms for Unachievable Tracking Problems

doi: 10.1109/JAS.2023.123756

Funds: This work was supported by the National Natural Science Foundation of China (62173333, 12271522), Beijing Natural Science Foundation (Z210002), and the Research Fund of Renmin University of China (2021030187)

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Author Bio:
Zeyi Zhang received the B. S. degree in mathematics from Qingdao University in 2020. He is currently working toward the Ph.D. degree with the School of Mathematics, Renmin University of China. His research interests include learning control and iterative methods

Hao Jiang received the B. S. degree from the Harbin Institute of Technology in 2009, and the Ph.D. degree from the University of Hong Kong, Hong Kong, China, in 2013. She is an Associate Professor with the School of Mathematics, Renmin University of China. Her research interests include learning-based modeling, optimization, and control of complex systems

Dong Shen (Senior Member, IEEE) received the B. S. degree in mathematics from School of Mathematics, Shandong University, in 2005, and the Ph.D. degree in mathematics from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences (CAS), in 2010. From 2010 to 2012, he was a Post-Doctoral Fellow with the Institute of Automation, CAS. From 2012 to 2019, he was with the College of Information Science and Technology, Beijing University of Chemical Technology. In 2016 and 2019, he was a Visiting Scholar with the National University of Singapore, Singapore, and RMIT University, Australia, respectively. Since 2020, he has been a Professor with the School of Mathematics, Renmin University of China. His research interests include iterative learning control, stochastic optimization, stochastic systems, and distributed artificial intelligence. He is currently serving on the Editorial Board of International Journal of Robust and Nonlinear Control and IET Cyber-Systems and Robotics, and Early Career Advisory Board of IEEE/CAA Journal of Automatica Sinica

Samer S. Saab (Senior Member, IEEE) is a Professor of electrical engineering at the Lebanese American University in Byblos, Lebanon. He joined the faculty in 1996 and has since made significant contributions to the university. Dr. Saab served as the Chairperson of the Department of Electrical and Computer Engineering from 2005 to 2012 and later held the position of Associate Dean in the School of Engineering from 2012 to 2013. Since October 2017, he has been fulfilling the role of Dean of Graduate Studies and Research, overseeing the university’s commitment to excellence in advanced education and research endeavors.Prior to his academic career, Dr. Saab gained valuable industry experience at Union Switch and Signal and ABB Daimler-Benz Transportation in Pittsburgh, PA from 1993 to 1996. He holds a B.S., M.S., and Ph.D. in electrical engineering, received in 1988, 1989, and 1992, respectively, from the University of Pittsburgh, USA. Additionally, he obtained an M.A. degree in applied mathematics in 1990 from the same institution. Dr. Saab’s research interests encompass various areas, including optimal stochastic control, navigational positioning systems, control of robot manipulators, and managerial policy design.Throughout his career, Dr. Saab has actively contributed to the academic community. He served on the Editorial Board of the IEEE Transactions on Control Systems Technology from 2005 to 2011, the Editorial Board of the IEEE Control Systems Society-Conference from 2005 to 2009, and the Editorial Board of the IEEE Transactions on Automatic Control from 2015 to 2022
Corresponding author: Dong Shen, e-mail: dshen@ruc.edu.cn
Received Date: 2023-06-04
Revised Date: 2023-06-26
Accepted Date: 2023-07-06

Available Online: 2023-09-21

Abstract

Abstract

For unachievable tracking problems, where the system output cannot precisely track a given reference, achieving the best possible approximation for the reference trajectory becomes the objective. This study aims to investigate solutions using the P-type learning control scheme. Initially, we demonstrate the necessity of gradient information for achieving the best approximation. Subsequently, we propose an input-output-driven learning gain design to handle the imprecise gradients of a class of uncertain systems. However, it is discovered that the desired performance may not be attainable when faced with incomplete information. To address this issue, an extended iterative learning control scheme is introduced. In this scheme, the tracking errors are modified through output data sampling, which incorporates low-memory footprints and offers flexibility in learning gain design. The input sequence is shown to converge towards the desired input, resulting in an output that is closest to the given reference in the least square sense. Numerical simulations are provided to validate the theoretical findings.
- Data-driven algorithms,
- incomplete information,
- iterative learning control,
- gradient information,
- unachievable problems

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References

[1]	D. A. Bristow, M. Tharayil, and A. G. Alleyne, “A survey of iterative learning control,” IEEE Control Systems, vol. 26, no. 3, pp. 96–114, 2006. doi: 10.1109/MCS.2006.1636313
[2]	S. R. Nekoo, J. Á. Acosta, G. Heredia, and A. Ollero, “A PD-type state-dependent riccati equation with iterative learning augmentation for mechanical systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 8, pp. 1499–1511, 2022. doi: 10.1109/JAS.2022.105533
[3]	D. Shen and C. Zhang, “Zero-error tracking control under unified quantized iterative learning framework via encodingdecoding method,” IEEE Trans. Cybernetics, vol. 52, no. 4, pp. 1979–1991, 2022. doi: 10.1109/TCYB.2020.3004187
[4]	D. Shen, N. Huo, and S. S. Saab, “A probabilistically quantized learning control framework for networked linear systems,” IEEE Trans. Neural Networks and Learning Systems, vol. 33, no. 12, pp. 7559–7573, 2022. doi: 10.1109/TNNLS.2021.3085559
[5]	D. Shen and Y. Xu, “Iterative learning control for discrete-time stochastic systems with quantized information,” IEEE/CAA J. Autom. Sinica, vol. 3, no. 1, pp. 59–67, 2016. doi: 10.1109/JAS.2016.7373763
[6]	S. S. Saab, “Stochastic P-type/D-type iterative learning control algorithms,” Int. Journal of Control, vol. 76, no. 2, pp. 139–148, 2003. doi: 10.1080/0020717031000077717
[7]	X. Dai, S. Tian, Y. Peng, and W. Luo, “Closed-loop P-type iterative learning control of uncertain linear distributed parameter systems,” IEEE/CAA J. Autom. Sinica, vol. 1, no. 3, pp. 267–273, 2014. doi: 10.1109/JAS.2014.7004684
[8]	D. Meng and K. L. Moore, “Robust iterative learning control for nonrepetitive uncertain systems,” IEEE Trans. Automatic Control, vol. 62, no. 2, pp. 907–913, 2017. doi: 10.1109/TAC.2016.2560961
[9]	C. Liu and X. Ruan, “Input-output-driven gain-adaptive iterative learning control for linear discrete-time-invariant systems,” Int. J. Robust and Nonlinear Control, vol. 31, no. 17, pp. 8551–8568, 2021. doi: 10.1002/rnc.5753
[10]	R. Chi, H. Zhang, B. Huang, and Z. Hou, “Quantitative data-driven adaptive iterative learning control: From trajectory tracking to point-to-point tracking,” IEEE Trans. Cybernetics, vol. 52, no. 6, pp. 4859–4873, 2022. doi: 10.1109/TCYB.2020.3015233
[11]	S. He, W. Chen, D. Li, Y. Xi, Y. Xu, and P. Zheng, “Iterative learning control with data-driven-based compensation,” IEEE Trans. Cybernetics, vol. 52, no. 8, pp. 7492–7503, 2022. doi: 10.1109/TCYB.2020.3041705
[12]	C. Hu, R. Zhou, Z. Wang, Y. Zhu, and M. Tomizuka, “Real-time iterative compensation framework for precision mechatronic motion control systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 7, pp. 1218–1232, 2022. doi: 10.1109/JAS.2022.105689
[13]	X. Bu, Z. Hou, S. Jin, and R. Chi, “An iterative learning control design approach for networked control systems with data dropouts,” Int. J. Robust and Nonlinear Control, vol. 26, no. 1, pp. 91–109, 2016. doi: 10.1002/rnc.3300
[14]	J. Chen, C. Hua, and X. Guan, “Iterative learning model-free control for networked systems with dual-direction data dropouts and actuator faults,” IEEE Trans. Neural Networks and Learning Systems, vol. 32, no. 11, pp. 5232–5240, 2021. doi: 10.1109/TNNLS.2020.3027651
[15]	H.-S. Ahn, K. L. Moore, and Y. Chen, “Stability of discrete-time iterative learning control with random data dropouts and delayed controlled signals in networked control systems,” in Proc. 10th Int. Conf. Control, Automation, Robotics and Vision, 2008, pp. 757–762.
[16]	J. Liu and X. Ruan, “Networked iterative learning control design for discrete-time systems with stochastic communication delay in input and output channels,” Int. J. Systems Science, vol. 48, no. 9, pp. 1844–1855, 2017. doi: 10.1080/00207721.2017.1289567
[17]	X. Li, J.-X. Xu, and D. Huang, “An iterative learning control approach for linear systems with randomly varying trial lengths,” IEEE Trans. Automatic Control, vol. 59, no. 7, pp. 1954–1960, 2014. doi: 10.1109/TAC.2013.2294827
[18]	D. Shen and S. S. Saab, “Noisy-output-based direct learning tracking control with Markov nonuniform trial lengths using adaptive gains,” IEEE Trans. Automatic Control, vol. 67, no. 8, pp. 4123–4130, 2022. doi: 10.1109/TAC.2021.3106860
[19]	X. Li, K. Wang, and D. Liu, “An improved result of multiple model iterative learning control,” IEEE/CAA J. Autom. Sinica, vol. 1, no. 3, pp. 315–322, 2014. doi: 10.1109/JAS.2014.7004689
[20]	D. Shen, G. Qu, and X. Yu, “Averaging techniques for balancing learning and tracking abilities over fading channels,” IEEE Trans. Automatic Control, vol. 66, no. 6, pp. 2636–2651, 2021. doi: 10.1109/TAC.2020.3011329
[21]	S. Zhu, X. Wang, and H. Liu, “Observer-based iterative and repetitive learning control for a class of nonlinear systems,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 5, pp. 990–998, 2018. doi: 10.1109/JAS.2017.7510463
[22]	G. Qu and D. Shen, “Stochastic iterative learning control with faded signals,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1196–1208, 2019. doi: 10.1109/JAS.2019.1911696
[23]	D. Shen and X. Yu, “Learning tracking over unknown fading channels based on iterative estimation,” IEEE Trans. Neural Networks and Learning Systems, vol. 33, no. 1, pp. 48–60, 2022. doi: 10.1109/TNNLS.2020.3027475
[24]	Y. Chen, C. Wen, Z. Gong, and M. Sun, “An iterative learning controller with initial state learning,” IEEE Trans. Automatic Control, vol. 44, no. 2, pp. 371–376, 1999. doi: 10.1109/9.746269
[25]	Y. Hui, R. Chi, B. Huang, and Z. Hou, “Extended state observer-based data-driven iterative learning control for permanent magnet linear motor with initial shifts and disturbances,” IEEE Trans. Systems,Man,and Cybernetics: Systems, vol. 51, no. 3, pp. 1881–1891, 2021. doi: 10.1109/TSMC.2019.2907379
[26]	X. He, Z. Sun, Z. Geng, and A. Robertsson, “Exponential set-point stabilization of underactuated vehicles moving in three-dimensional space,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 2, pp. 270–282, 2022. doi: 10.1109/JAS.2021.1004323
[27]	D. Shen, C. Liu, L. Wang, and X. Yu, “Iterative learning tracking for multisensor systems: A weighted optimization approach,” IEEE Trans. Cybernetics, vol. 51, no. 3, pp. 1286–1299, 2021. doi: 10.1109/TCYB.2019.2942105
[28]	Z. Zhang, H. Jiang, and D. Shen, “Extended iterative learning control for inconsistent tracking problems with random dropouts,” in Proc. IEEE 11th Data Driven Control and Learning Systems Conf., 2022, pp. 935–940.
[29]	R. Chi, Z. Hou, B. Huang, and S. Jin, “A unified data-driven design framework of optimality-based generalized iterative learning control,” Computers &Chemical Engineering, vol. 77, pp. 10–23, 2015.
[30]	L. Ma, X. Liu, X. Kong, and K. Y. Lee, “Iterative learning model predictive control based on iterative data-driven modeling,” IEEE Trans. Neural Networks and Learning Systems, vol. 32, no. 8, pp. 3377–3390, 2021. doi: 10.1109/TNNLS.2020.3016295
[31]	S. S. Saab, D. Shen, M. Orabi, D. Kors, and R. H. Jaafar, “Iterative learning control: Practical implementation and automation,” IEEE Trans. Industrial Electronics, vol. 69, no. 2, pp. 1858–1866, 2022. doi: 10.1109/TIE.2021.3063866
[32]	R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge University Press, 1985.
[33]	D. Shen, “Iterative learning control with incomplete information: A survey,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 5, pp. 885–901, 2018. doi: 10.1109/JAS.2018.7511123
[34]	H.-S. Ahn, K. Moore, and Y. Chen, “Monotonic convergent iterative learning controller design based on interval model conversion,” IEEE Trans. Automatic Control, vol. 51, no. 2, pp. 366–371, 2006. doi: 10.1109/TAC.2005.863498
[35]	H.-S. Ahn, K. L. Moore, and Y. Chen, “Stability analysis of discrete-time iterative learning control systems with interval uncertainty,” Automatica, vol. 43, no. 5, pp. 892–902, 2007. doi: 10.1016/j.automatica.2006.11.020
[36]	J. H. Lee, K. S. Lee, and W. C. Kim, “Model-based iterative learning control with a quadratic criterion for time-varying linear systems,” Automatica, vol. 36, no. 5, pp. 641–657, 2000. doi: 10.1016/S0005-1098(99)00194-6

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characterize the concept of the unachievable tracking problem
demonstrate the necessity of gradient information in achieving the control objective
Introduce a design for an input-output-driven learning gain matrix
Identify the gradient drift problem arising from incomplete data
Propose an extended ILC scheme incorporating an error compensation mechanism

Data-Driven Learning Control Algorithms for Unachievable Tracking Problems

doi: 10.1109/JAS.2023.123756

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通讯作者: 陈斌, bchen63@163.com

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