Forgetting Factor Nonlinear Functional Analysis for Iterative Learning System with Time-Varying Disturbances and Unknown Uncertain
Automation, Control and Intelligent Systems
Volume 5, Issue 3, June 2017, Pages: 33-43
Received: Apr. 18, 2017;
Accepted: Apr. 27, 2017;
Published: Jun. 21, 2017
Views 1962 Downloads 59
Wei Zheng, Department of Electrical Engineering, Yanshan University, Qinhuangdao, China
Hong-Bin Wang, Department of Electrical Engineering, Yanshan University, Qinhuangdao, China; Liren Institute, Yanshan University, Qinhuangdao, China
Shu-Huan Wen, Department of Electrical Engineering, Yanshan University, Qinhuangdao, China
Zhi-Ming Zhang, China National Heavy Machinery Research Institute, Xi'an, China
This paper focuses on the iterative learning tracking control problem for a class of nonlinear system with time-varying disturbances. First, because of the mismatches in time-varying disturbances functions, a high-order feed-forward iterative learning control (ILC) is employed to change the original system into an iterative system. Secondly, a variable forgetting factor is developed to stabilize the system. Based on the feed-forward iterative learning controller, a memory controller is constructed for the nonlinear system. By choosing a new variable forgetting factor, we show that the designed continuous adaptive controller makes the solutions of the closed-loop system convergent to a ball exponentially. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed method.
Forgetting Factor Nonlinear Functional Analysis for Iterative Learning System with Time-Varying Disturbances and Unknown Uncertain, Automation, Control and Intelligent Systems.
Vol. 5, No. 3,
2017, pp. 33-43.
D. Best, J. Liu, L. Rene, and R. V. D. Molengraft, "Second-order iterative learning control for scaled setpoints," IEEE Trans. Contr. Syst. Tech., vol. 23, no. 2, pp. 805-812, Mar. 2015.
S. Arimoto, M. Sekimoto, K. Tahara, "Iterative learning without reinforcement or reward for multijoint movements: a revisit of bernstein's DOF problem on dexterity," Journal of Robotics, vol. 2016, Article ID 2016315, pp. 1-11, May. 2016.
T. Abdelhamid, "Adaptive iterative learning control for robot manipulators," Automatica, vol. 40, no. 7, pp. 1195-1203, Jul. 2004.
P. Sampson, C. Freeman, S. Coote, and S. Demain,“Using functional electrical stimulation mediated by iterative learning control and robotics to improve arm movement for people with multiple sclerosis,” IEEE Trans. Neur. Syst. Reh., vol. 24, no. 2, pp. 235-248, Feb. 2015.
C. Li, L. Chang, Z. Huang, Y. Liu, and N. Zhang,"Parameter identification of a nonlinear model of hydraulic turbine governing system with an elastic water hammer based on a modified gravitational search algorithm," Eng. Appl. Artif. Intel., vol. 50, pp. 177-191, Apr. 2016.
H. Q. 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. 2013.
A. Tayebi, and C. J. Chien, "A unified adaptive iterative learning control framework for uncertain nonlinear systems," IEEE Trans. Autom. Control, vol. 52, no. 10, pp. 1907-1913, Oct. 2007.
K. L. Moore, Y. Q. Chen, and V. Bahl, "Monotonically convergent iterative learning control for linear discrete-time systems," Automatica, vol. 41, no. 9, pp. 1529-1537, Sep. 2005.
D. Huang, J. X. Xu, V. Venkataramanan, and T. C. T. Huynh, "High-performancetracking of piezoelectric positioning stage using current-cycle iterative learning control with gain scheduling," IEEE Tans. Indus. Electr., vol. 61, no. 2, pp. 1085-1098, Feb. 2014.
X. Bu and Z. Hou, “Adaptive iterative learning control for linear systems with binary-valued observations,” IEEE Trans. Neur. Net. Lear., vol. 99, pp. 1-6, Nov. 2016.
J. Zhou, H. Yue, J. Zhang, and H. Wang, “Iterative learning double closed-loop structure for modeling and controller design of output stochastic distribution control systems,” IEEE Tans. Contr. Sys. Tech., vol. 22, no. 6, pp. 2261-2276, Nov. 2014.
Q. Zhu, J. X. Xu, D. Huang, and G. D. Hu, “Iterative learning control design for linear discrete-time systems with multiple high-order internal models,” Automatica, vol. 62, no. C, pp. 65-76, Dec. 2015.
G. Pipeleers, and K. L, “Moore reduced-order iterative learning control and a design strategy for optimal performance tradeoffs,” IEEE Trans. Autom. Control, vol. 57, no. 9, pp. 2390-2395, Sep. 2012.
X. Jin, “Adaptive iterative learning control for high-order nonlinear multi-agent systems consensus tracking,” Syst. Control Lett., vol. 89, pp. 16-23, Mar. 2016.
A. Luo, X. Xu, L. Fang, and H. Fang, “Feedback-feedforward pi-type iterative learning control strategy for hybrid active power filter with injection circuit,” IEEE Trans. Ind. Electron., vol. 57, no. 11, pp. 3767-3779, Nov. 2010.
Z. Li, Y. Hu, and D. Li, “Robust design of feedback feed-forward iterative learning control based on 2D system theory for linear uncertain systems,” Int. J. Syst. Sci., vol. 47, no. 11, pp. 2620-2631, Aug. 2015.
C. Paleologu, J. Benesty, and S. Ciochina, “A robust variable forgetting factor recursive least-squares algorithm for system identification,” IEEE Signal Proc. Let., vol. 15, pp. 597-600, Oct, 2008.
K. Zhang, C. R. Zhao, and X. J. Xie, “Global output feedback stabilisation of stochastic high-order feed forward nonlinear systems with time-delay,” Int. J. Control, vol. 88, no. 12, pp. 2477-2487, Dec. 2015.
R. M. Canetti and M. D. España, “Convergence analysis of the least-squares identification algorithm with a variable forgetting factor for time-varying linear systems,” Automatica, vol. 25, no. 4, pp. 609-612, Jul. 1989.
Z. Zhong, Y. Zhu, and T. Yang, “Robust decentralized static output-feedback control design for large-scale nonlinear systems using takagi-sugeno fuzzy models,” IEEE Access, vol. 4, pp. 8250-8263, Nov. 2016.
W. Paszke, S. Hao, K. Galkowski, and T. Liu, “Robust iterative learning control for batch processes with input delay subject to time-varying uncertainties,” IET Control Theory Appl., vol. 10, no. 15, pp. 1904-1915, Oct. 2016.
L. Lu, H. Zhao, and B. Chen, “Improved-variable-forgetting-factor recursive algorithm based on the logarithmic cost for volterra system identification,” IEEE Trans. Circuits-II, vol. 63, no. 6, pp. 588-592, Jun. 2016.
K. L. Barton and A. G. Alleyne, “A cross-coupled iterative learning control design for precision motion control,” IEEE Trans. Contr. Syst. Tech., vol. 16, no. 6, pp. 1218 – 1231, Nov. 2008.