Abstract
In this paper, a direct adaptive neural network control algorithm based on the backstepping technique is proposed for a class of uncertain nonlinear discrete-time systems in the strict-feedback form. The neural networks are utilized to approximate unknown functions, and a stable adaptive neural network controller is synthesized. The fact that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded is proven and the tracking error can converge to a small neighborhood of zero by choosing the design parameters appropriately. Compared with the previous research for discrete-time systems, the proposed algorithm improves the robustness of the systems. A simulation example is employed to illustrate the effectiveness of the proposed algorithm.
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References
Park J, Sandberg IW (1991) Universal approximation using radial-basis-function network. Neural Comput 3(2):246–257
Wang LX (1992) Fuzzy systems are universal approximators. In: Proceedings of the IEEE international conference fuzzy systems. San Diego, CA, pp 1163–1170
Li TS, Tong SC, Feng G (2010) A novel robust adaptive-fuzzy-tracking control for a class of nonlinear multi-input/multi-output systems. IEEE Trans Fuzzy Syst 18(1):150–160
Liu YJ, Tong SC, Wang W (2009) Adaptive fuzzy output tracking control for a class of uncertain nonlinear systems. Fuzzy Sets Syst 160(9):2727–2754
Chen WS, Jiao LC, Li RH, Li J (2010) Adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances. IEEE Trans Fuzzy Syst 18(4):674–685
Ge SS, Wang C (2004) Adaptive neural control of uncertain MIMO nonlinear systems. IEEE Trans Neural Netw 15(3):674–692
Tong SC, Li CY, Li YM (2009) Fuzzy adaptive observer backstepping control for MIMO nonlinear systems. Fuzzy Sets Syst 160(19):2755–2775
Li ZJ, Chen WD (2008) Adaptive neural-fuzzy control of uncertain constrained multiple coordinated nonholonomic mobile manipulators. Eng Appl Artif Intell 21(7):985–1000
Li ZJ, Xu CQ (2009) Adaptive fuzzy logic control of dynamic balance and motion for wheeled inverted pendulums. Fuzzy Sets Syst 160(12):1787–1803
Chen WS, Li JM (2008) Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Trans Syst Man Cybern B Cybern 38(1):258–266
Chen WS, Jiao LC (2010) Adaptive tracking for periodically time-varying and nonlinearly parameterized systems using multilayer neural networks. IEEE Trans Neural Netw 21(2):345–351
Tong SC, He XL, Zhang HG (2009) Combined backstepping and small-gain approach to robust adaptive fuzzy output feedback control. IEEE Trans Fuzzy Syst 17(5):1059–1069
Tong SC, He XL, Li YM, Zhang HG (2010) Adaptive fuzzy backstepping robust control for uncertain nonlinear systems based on small-gain approach. Fuzzy Sets Syst 161(3):771–796
Li HX, Tong SC (2003) A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems. IEEE Trans Fuzzy Syst 11(1):24–34
Zhang HG, Cai LL, Bien Z (2000) A fuzzy basis function vector-based multivariable adaptive fuzzy controller for nonlinear systems. Trans Syst Man Cybern B Cybern 30(1):210–217
Zhang HG, Bien Z (2000) Adaptive fuzzy control of MIMO nonlinear systems. Fuzzy Sets Syst 115(2):191–204
Liu YJ, Wang W (2007) Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems. Inf Sci 177(18):3901–3917
Ge SS, Lee TH, Li GY, Zhang J (2003) Adaptive NN control for aclass of discrete-time nonlinear systems. Int J Control 76(4):334–354
Yang CG, Ge SS, Xiang C, Chai TY, Lee TH (2008) Output feedback NN control for two classes of discrete-time systems with unknown control directions in a unified approach. IEEE Trans Neural Netw 19(11):1873–1886
Zhang J, Ge SS, Lee TL (2005) Output feedback control of a class of discrete MIMO nonlinear systems with triangular form inputs. IEEE Trans Neural Netw 16(6):1491–1503
Ge SS, Li GY, Lee TH (2003) Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems. Automatica 39(5):807–819
Ge SS, Zhang J, Lee TH (2004) State feedback neural network control of a class of discrete MIMO nonlinear systems with disturbances. IEEE Trans Syst Man Cybern B Cybern 34(4):1630–1645
Ge SS, Li GY, Zhang J, Lee TH (2004) Direct adaptive control for a class of MIMO nonlinear systems using neural networks. IEEE Trans Autom Control 49(11):2001–2006
Liu YJ, Wen GX, Tong SC (2010) Direct adaptive NN control for a class of discrete-time nonlinear strict-feedback systems. Neurocomputing 73(13–15):2498–2505
Diaz DV, Tang Y (2004) Adaptive robust fuzzy control of nonlinear systems. IEEE Trans Syst Man Cyber B Cybern 34(3):1596–1601
Ge SS, Wang J (2002) Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems. IEEE Trans Neural Netw 13(6):1409–1419
Liu YJ, Wang W, Tong SC, Liu YS (2010) Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters. IEEE Trans Syst Man Cybern A Syst Hum 40(1):170–184
Acknowledgments
The authors would like to thank the valuable comments and also appreciate the constructive suggestions from the anonymous referees. This research was supported by the Natural Science Foundation of China under Grant 61074014 and 60874056; The Chinese National Basic Research 973 Program under Grant 2011CB302801; Macau Science and Technology Development Foundation under Grant 008/2010/A1; The Science Foundation of Educational Department of Liaoning Province under Grant L2010181; The Natural Science Foundation of Liaoning Province under Grant 20102095.
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Wen, GX., Liu, YJ. & Philip Chen, C.L. Direct adaptive robust NN control for a class of discrete-time nonlinear strict-feedback SISO systems. Neural Comput & Applic 21, 1423–1431 (2012). https://doi.org/10.1007/s00521-011-0596-4
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DOI: https://doi.org/10.1007/s00521-011-0596-4