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Machine Intelligence Research

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01-06-2013

Adaptive Tracking Control of Uncertain MIMO Nonlinear Systems with Time- varying Delays and Unmodeled Dynamics

Authors: Xiao-Cheng Shi, Tian-Ping Zhang

Published in: Machine Intelligence Research | Issue 3/2013

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Abstract

In this paper, adaptive neural tracking control is proposed based on radial basis function neural networks (RBFNNs) for a class of multi-input multi-output (MIMO) nonlinear systems with completely unknown control directions, unknown dynamic disturbances, unmodeled dynamics, and uncertainties with time-varying delay. Using the Nussbaum function properties, the unknown control directions are dealt with. By constructing appropriate Lyapunov-Krasovskii functionals, the unknown upper bound functions of the time-varying delay uncertainties are compensated. The proposed control scheme does not need to calculate the integral of the delayed state functions. Using Young’s inequality and RBFNNs, the assumption of unmodeled dynamics is relaxed. By theoretical analysis, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded.

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[1]

S. S. Ge, C. C. Huang, T. Zhang. Adaptive neural network control of nonlinear systems by state and output feedback. IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics, vol. 29, no. 6, pp. 818–828, 1999.CrossRef

[2]

S. S. Ge, C. Wang, T. H. Lee. Adaptive backstepping control of a class of chaotic systems. International Journal of Bifurcation and Chaos, vol. 10, no. 5, pp. 1149–1156, 2000.CrossRefMATHMathSciNet

[3]

S. S. Ge, C. C. Huang, T. Zhang. Nonlinear adaptive control using neural networks and its application to CSTR systems. Journal of Process Control, vol. 9, no. 4, pp. 313–323, 1999.CrossRef

[4]

T. Zhang, S. S. Ge, C. C. Hang. Adaptive neural network control for strict-feedback nonlinear systems using back-stepping design. Automatica, vol. 36, no. 12, pp. 1835–1846, 2000.CrossRefMATHMathSciNet

[5]

I. Mizumoto, T. W Chen, S. Ohdaira, K. Makoto, I. Zenta. Adaptive output feedback control of general MIMO systems using multirate sampling and its application to a cart-crane system. Automatica, vol. 43, no. 12, pp. 2077–2085, 2007.CrossRefMATHMathSciNet

[6]

T. P. Zhang, S. S. Ge. Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs. Automatica, vol. 43, no. 6, pp. 1021–1033, 2007.CrossRefMATHMathSciNet

[7]

H. B. Qian, T. P. Zhang. Adaptive control of MIMO nonlinear time-varying delay systems with unknown gain signs. Control and Decision, vol. 23, no. 10, pp. 1153–1158, 2008. (in Chinese)MathSciNet

[8]

S. S. Ge, F. Hong, T. H. Lee. Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients. IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics, vol. 34, no. 1, pp. 499–516, 2004.CrossRefMathSciNet

[9]

J. Hale. Theory of Functional Differential Equations, New York: Springer, 1977.CrossRefMATH

[10]

M. Jankovic. Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems. IEEE Transactions on Automatic Control, vol. 46, no. 7, pp. 1048–1060, 2001.CrossRefMATHMathSciNet

[11]

S. S. Ge, F. Hong, T. H. Lee. Robust adaptive control of nonlinear systems with unknown time delays. Automatica, vol. 41, no. 7, pp. 1181–1190, 2005.CrossRefMATHMathSciNet

[12]

S. S. Ge, K. P. Tee. Approximation-based control of nonlinear MIMO time-delay systems. Automatica, vol. 43, no. 1, pp. 31–43, 2007.CrossRefMATHMathSciNet

[13]

M. Wang, B. Chen, K. F. Liu, S. Y. Zhang. Adaptive fuzzy tracking control of nonlinear time-delay systems with unknown virtual control coefficients. Information Sciences, vol. 178, no. 22, pp. 4326–4340, 2008.CrossRefMATHMathSciNet

[14]

Q. Q. Zhu, T. P. Zhang, B. C. Zhu. Adaptive control of MIMO nonlinear systems with disturbances and time delays. In Proceedings of the Chinese Control and Decision Conference, IEEE, Xuzhou, China, pp. 199–204, 2010.

[15]

T. P. Zhang, C. Y. Zhou, Q. Zhu. Adaptive variable structure control of MIMO nonlinear systems with time-varying delays and unknown dead-zones. International Journal of Automation and Computing, vol. 6, no. 2, pp. 124–136, 2009.CrossRef

[16]

H. Y. Yue, J. M. Li. Adaptive fuzzy dynamic surface control for a class of perturbed nonlinear time-varying delay systems with unknown dead-zone. International Journal of Automation and Computing, vol. 9, no. 5, pp. 545–554, 2012.CrossRef

[17]

D. Li, J. M. Li. Adaptive iterative learning control for non-linearly parameterized systems with unknown time-varying delay and unknown control direction. International Journal of Automation and Computing, vol.9, no. 6, pp. 578–586, 2012.CrossRef

[18]

S. C. Tong, X. L. He, Y. M. Li, H. G. Zhang. Adaptive fuzzy backstepping robust control for uncertain nonlinear systems based on small-gain approach. Fuzzy Sets and Systems, vol. 161, no. 6, pp. 771–796, 2010.CrossRefMATHMathSciNet

[19]

S. C. Tong, Y. M. Li. Fuzzy adaptive robust backstepping stabilization for SISO nonlinear systems with unknown virtual control direction. Information Sciences, vol. 180, no. 23, pp. 4619–4640, 2010.CrossRefMATHMathSciNet

[20]

T. P. Zhang, Y. Lu. Adaptive dynamic surface control of nonlinear systems with unmodeled dynamics. Control and Decision, vol. 27, no. 3, pp. 335–342, 2012. (in Chinese)MATHMathSciNet

[21]

Z. P. Jiang, D. J. Hill. A robust adaptive backstepping scheme for nonlinear systems with unmodeled dynamics. IEEE Transactions on Automatic Control, vol. 44, no. 9, pp. 1705–1711, 1999.CrossRefMATHMathSciNet

[22]

M. Krstic, I. Kanellakopoulos, P. V. Kokotovic. Nonlinear and Adaptive Control Design, New York: Wiley, 1995.

[23]

R. M. Sanner, J. J. E. Slotine. Gaussian networks for direct adaptive control. IEEE Transactions on Neural Networks, vol. 3, no. 6, pp. 837–863, 1992.CrossRef

[24]

S. S. Ge, C. C. Hang, T. H. Lee, T. Zhang. Stable Adaptive Neural Network Control, Boston: Kluwer Academic, pp. 27–46, 2001.

Title: Adaptive Tracking Control of Uncertain MIMO Nonlinear Systems with Time- varying Delays and Unmodeled Dynamics
Authors: Xiao-Cheng Shi
Tian-Ping Zhang
Publication date: 01-06-2013
Publisher: Springer-Verlag
Published in: Machine Intelligence Research / Issue 3/2013
Print ISSN: 2731-538X
Electronic ISSN: 2731-5398
DOI: https://doi.org/10.1007/s11633-013-0712-2

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