Non-uniform Trajectory Tracking AILC for Nonlinear Time-varying Parameter System with Multiple Unknown Control Directions

Chunli Zhang; Yangjie Gao; Lei Yan

doi:10.61383/ejam.20231127

Authors

Chunli Zhang Xi’an University of Technology, Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing Corresponding Author
Yangjie Gao Xi’an University of Technology, Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing
Lei Yan Xi’an University of Technology, Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing

DOI:

https://doi.org/10.61383/ejam.20231127

Keywords:

Iterative learning control, Time-varying parameter systems, Lyapunov-like, Multiple unknown control directions, Non-uniform target tracking

Abstract

In this paper, a new iterative learning controller is presented for nonlinear time-varying parameter system to solve the tracking problem of different target trajectories. Based on Nussbaum function and the Lyapunov-like synthesis design the learning controller to handle system dynamics with multi-unknown control directions. Over a finite time interval, the unknown time-varying parameter is considered to be periodic, so it is expanded using a Fourier series expansion, and the remaining terms are treated with a canonical series. The controller designed in this paper can ensure that all signals of the closed-loop system are bounded in a finite time interval [0,T], and can complete non-uniform target tracking. Finally, a simulation example is given to verify the effectiveness of the designed controller.

References

[1] Rosales, Claudio, Miguel Soria,etc. Identification and adaptive PID Control of a hexacopter UAV based on neural networks[J]. International journal of adaptive control and signal processing,2019,33(1):74-91. DOI: https://doi.org/10.1002/acs.2955

[2] O. Koc, G. Maeda and J. Peters. Optimizing the Execution of Dynamic Robot Movements With Learning Control[J]. IEEE Transactions on Robotics, 2019,35(4): 909-924. DOI: https://doi.org/10.1109/TRO.2019.2906558

[3] L. Bingqiang, L. Tianyi, Z. Yiyun and L. Shuaishuai. Open-loop and closed-loop D-type iterative learning control for fractional-order linear multi-agent systems with state-delays [J]. Journal of Systems Engineering and Electronics, 2021, 32(1):197-208. DOI: https://doi.org/10.23919/JSEE.2021.000017

[4] Q. Yu and Z. Hou. Adaptive Fuzzy Iterative Learning Control for High-Speed Trains With Both Randomly Varying Operation Lengths and System Constraints[J]. IEEE Transactions on Fuzzy Systems, 2021,29(8):2408 2418. DOI: https://doi.org/10.1109/TFUZZ.2020.2999958

[5] S. Jingzhuo and W. Huang. Predictive Iterative Learning Speed Control With On-Line Identification for Ultrasonic Motor[J]. IEEE Access, 2020, 8:78202-78212. DOI: https://doi.org/10.1109/ACCESS.2020.2989866

[6] French M and Rogers E. Nonlinear iterative learning by an adaptive lyapunov technique[J]. Int. J. Control,2000, 73(10):840-850. DOI: https://doi.org/10.1080/002071700405824

[7] G. Li. High-order iterative learning control for nonlinear systems[C]. 2017 6th Data Driven Control and Learning Systems (DDCLS), 2017:191-196. DOI: https://doi.org/10.1109/DDCLS.2017.8068067

[8] G. Liu and Z. Hou. Iterative Learning based Model Free Adaptive Control for Subway Trains with Speed and Input Constraints[C]. 2019 Chinese Control Conference (CCC), 2019:2436-2441. DOI: https://doi.org/10.23919/ChiCC.2019.8866193

[9] L. Wu, Q. Yan and J. Cai. Neural Network-Based Adaptive Learning Control for Robot Manipulators With Arbitrary Initial Errors[J]. IEEE Access, 2019, 7: 180194-180204. DOI: https://doi.org/10.1109/ACCESS.2019.2958371

[10] Z. Zhou, W. Wang, Y. Zhang, Q. Yan and J. Cai. Barrier Adaptive Iterative Learning Control for Tank Gun Control Systems Under Nonzero Initial Error Condition[J]. IEEE Access, 2022, 10: 8664-8672. DOI: https://doi.org/10.1109/ACCESS.2022.3144326

[11] Chunli Zhang, Junmin Li. Adaptive Iterative Learning Control of Non-uniform Trajectory Tracking for Strict Feedback Nonlinear Time-varying Systems[J]. International Journal of Automation and Computing, 2014, 11(6): 621-626. DOI: https://doi.org/10.1007/s11633-014-0819-0

[12] J. Xu. Fault-tolerant iterative learning control for mobile robots non-repetitive trajectory tracking with output constraints[J]. Automatica, 2018, 94: 63-71. DOI: https://doi.org/10.1016/j.automatica.2018.04.011

[13] Chunli Zhang, Junmin Li. Adaptive Iterative Learning Control of Non-uniform Trajectory Tracking for Strict Feedback Nonlinear Time-varying Systems with Unknown Control Direction[J]. Applied Mathematical Modelling,2015,39: 2942-2950. DOI: https://doi.org/10.1016/j.apm.2014.10.070

[14] Ye Xudong and Jiang Jingping. Adaptive nonlinear design without a priori knowledge of control directions[J]. IEEE Transactions on Automatic Control, 1998, 43(11): 1617-1621. DOI: https://doi.org/10.1109/9.728882

[15] S. S. Ge and J. Wang. Robust adaptive tracking for time-varying uncertain nonlinear systems with unknown control coefficients[J]. IEEE Transactions on Automatic Control, 2003, 48(8):1463-1469. DOI: https://doi.org/10.1109/TAC.2003.815049

[16] Y. Miao, H. Chao, P. Junmin and Y. Xudong. Adaptive iterative learning control for discrete-time nonlinear systems with unknown control direction[C]. Proceedings of the 31st Chinese Control Conference, 2012:2906 2910.

[17] J. X. Xu, R. Yan. Iterative learning control design without a priori knowledge of the control direction[J]. Automatica, 2004, 40:1803-1809. DOI: https://doi.org/10.1016/j.automatica.2004.05.010

[18] C. Zhang, L. Yan, etc. A new adaptive iterative learning control of finite-time hybrid function projective syn chronization for unknown time-varying chaotic systems[J]. Front. Phys, 2023, doi: 10.3389/fphy.2023.1127884. DOI: https://doi.org/10.3389/fphy.2023.1127884