Observer-Based Adaptive Neural Iterative Learning Control for a Class of Time-Varying Nonlinear Systems

Expand
  • (1. Department of Control Engineering, Naval Aeronautical University, Yantai 264001, Shandong, China; 2. Department of Electrical and Electronic Engineering, Yantai Nanshan University, Yantai 265713, Shandong, China; 3. Shandong Nanshan International Flight Co., Ltd., Yantai 265713, Shandong, China)

Online published: 2017-06-04

Abstract

In this paper an adaptive iterative learning control scheme is presented for the output tracking of a class of nonlinear systems. An observer is designed to estimate the tracking errors. A mixed time domain and s-domain representation is constructed to derive an error model with relative degree one for our purpose. And time-varying radial basis function neural network is employed to deal with system uncertainty. A new signal is constructed by using a first-order filter, which removes the requirement of strict positive real (SPR) condition and identical initial condition of iterative learning control. Based on property of hyperbolic tangent function, the system tracing error is proved to converge to the origin as the iteration tends to infinity by constructing Lyapunov-like composite energy function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

Cite this article

WEI Jianming1* (韦建明), ZHANG Youan2 (张友安), LIU Jingmao3 (刘京茂) . Observer-Based Adaptive Neural Iterative Learning Control for a Class of Time-Varying Nonlinear Systems[J]. Journal of Shanghai Jiaotong University(Science), 2017 , 22(3) : 303 -312 . DOI: 10.1007/s12204-017-1836-2

References

[1] LEE H S, BIEN Z. A note on convergence property ofiterative learning controller with respect to sup norm[J]. Automatica, 1997, 33(8): 1591-1593. [2] CHEN Y Q, GONG Z M, WEN C Y. Analysis of ahigh-order iterative learning control algorithm for uncertainnonlinear systems with state delays [J]. Automatica,1998, 34(3): 345-353. [3] SUNM X,WANG DW. Iterative learning control withinitial rectifying action [J]. Automatica, 2002, 38(7):1177-1182. [4] CHIEN C J, LIU J S. A P-type iterative learning controllerfor robust output tracking of nonlinear timevaryingsystems [J]. International Journal of Control,1996, 64(2): 319-334. [5] XU J X, TAN Y. A composite energy functionbasedlearning control approach for nonlinear systemswith time-varying parametric uncertainties [J]. IEEETransactions on Automatic Control, 2002, 47(11):1940-1945. [6] XU J X, TAN Y, LEE T H. Iterative learning controldesign based on composite energy function with inputsaturation [J]. Automatica, 2004, 40(8): 1371-1377. [7] CHI R H, HOU Z S, XU J X. Adaptive ILC for aclass of discrete-time systems with iteration-varyingtrajectory and random initial condition [J]. Automatica,2008, 44(8): 2207-2213. [8] WANG Y C, CHIEN C J. Decentralized adaptive fuzzyneural iterative learning control for nonaffine nonlinearinterconnected systems [J]. Asian Journal of Control,2011, 13(1): 94-106. [9] XU J, XU J X. Iterative learning control for outputconstrainedsystems with both parametric and nonparametricuncertainties [J]. Automatica, 2013, 49(8):2508-2516. [10] ZHANG C L, LI J M. Adaptive iterative learning controlfor nonlinear pure-feedback systems with initialstate error based on fuzzy approximation [J]. Journalof the Franklin Institute, 2014, 351(3): 1483-1500. [11] LEU Y G, WANG W Y, LEE T T. Observer-baseddirect adaptive fuzzy-neural control for nonaffine nonlinearsystems [J]. IEEE Transaction on Neural Networks,2005, 16(4): 853-861. [12] LIU Y J, ZHOU N. Observer-based adaptive fuzzyneuralcontrol for a class of uncertain nonlinear systemswith unknown dead-zone input [J]. ISA Transactions,2010, 49(4): 462-469. [13] TONG S C, LI Y, LI Y M, et al. Observer-based adaptivefuzzy backstepping control for a class of stochasticnonlinear strict-feedback systems [J]. IEEE Transactionson Systems, Man, and Cybernetics. Part B:Cybernetics, 2011, 41(6): 1693-1704. [14] ZHOU B, LI Z Y, LIN Z L. Observer based outputfeedback control of linear systems with input and outputdelays [J]. Automatica, 2013, 49(7): 2039–2052. [15] DINH H T, KAMALAPURKAR R, BHASIN S, etal. Dynamic neural network-based robust observersfor uncertain nonlinear systems [J]. Neural Networks,2014, 60: 44-52. [16] HUA C C, YU C X, GUAN X P. Neural networkobserver-based networked control for a class of nonlinearsystems [J]. Neurocomputing, 2014, 133: 103-110. [17] WANG Q D, WEI C L. Decentralized robust adaptiveoutput feedback control of stochastic nonlinear interconnectedsystems with dynamic interactions [J]. Automatica,2015, 54: 124-134. [18] CHEN B, LIN C, LIU X P, et al. Observer-based adaptivefuzzy control for a class of nonlinear delayed systems[J]. IEEE Transactions on Systems, Man, andCybernetics: Systems, 2016, 46(1): 27-36. [19] TAYEBI A, XU J X. Observer-based iterative learningcontrol for a class of time-varying nonlinear systems[J]. IEEE Transactions on Circuits and Systems.I: Fundamental Theory and Applications, 2003, 50(3):452-455. [20] XU J X, XU J. Observer based learning control for aclass of nonlinear systems with time-varying parametricuncertainties [J]. IEEE Transactions on AutomaticControl, 2004, 49(2): 275-281. [21] WANG Y C, CHIEN C J. An observer based adaptiveiterative learning control for robotic systems [C]//2011IEEE International Conference on Fuzzy Systems.Taipei: IEEE, 2011: 2876-2881. [22] CHIEN C J, WANG Y C. An observer-based fuzzyneural network adaptive ILC for nonlinear systems[C]//13th International Conference on Control, Automationand Systems. Gwangju, Korea: IEEE, 2013:226-232. [23] WANG Y C, CHIEN C J, ER M J. An observer-basedadaptive iterative learning controller for MIMO nonlinearsystems with delayed output [C]//13th InternationalConference on Control, Automation, Roboticsand Vision. Singapore: IEEE, 2014: 157-162. [24] WANG Y C, CHIEN C J. An observer-based model referenceadaptive iterative learning controller for MIMOnonlinear systems [C]//11th IEEE International Conferenceon Control & Automation (ICCA). Taipei:IEEE, 2014: 1168-1173. [25] CHEN W S, LI R H, LI J. Observer-based adaptiveiterative learning control for nonlinear systems withtime-varying delays [J]. International Journal of Automationand Computing, 2010, 7(4): 438-446. [26] GE S S, HANG C C, LEE T H, et al. Stable adaptiveneural network control [M]. Norwell, USA: KluwerAcademic Publisher, 2001: 27-29. [27] POLYCARPOU M M. Stable adaptive neural controlscheme for nonlinear systems [J]. IEEE Transactionson Automatic Control, 1996, 41(3): 447-451.
Options
Outlines

/