×

Adaptive neural control for a class of outputs time-delay nonlinear systems. (English) Zbl 1264.93110

Summary: We consider an adaptive neural control for a class of outputs time-delay nonlinear systems with perturbed or no. Based on RBF neural networks, the radius basis function (RBF) neural networks is employed to estimate the unknown continuous functions. The proposed control guarantees that all closed-loop signals remain bounded. The simulation results demonstrate the effectiveness of the proposed control scheme.

MSC:

93C40 Adaptive control/observation systems
93C23 Control/observation systems governed by functional-differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] H. Fang and Z. Lin, “A further result on global stabilization of oscillators with bounded delayed input,” IEEE Transactions on Automatic Control, vol. 51, no. 1, pp. 121-128, 2006. · Zbl 1366.93498 · doi:10.1109/TAC.2005.861709
[2] Z. Lin and H. Fang, “On asymptotic stabilizability of linear systems with delayed input,” IEEE Transactions on Automatic Control, vol. 52, no. 6, pp. 998-1013, 2007. · Zbl 1141.93053 · doi:10.4310/CIS.2007.v7.n3.a2
[3] K. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-Delay Systems, Birkhauser, Boston, Mass, USA, 2003. · Zbl 1039.34067
[4] V. B. Kolmanovskii and J.-P. Richard, “Stability of some linear systems with delays,” IEEE Transactions on Automatic Control, vol. 44, no. 5, pp. 984-989, 1999. · Zbl 0964.34065 · doi:10.1109/9.763213
[5] Y.-J. Sun, J.-G. Hsieh, and H.-C. Yang, “On the stability of uncertain systems with multiple time-varying delays,” IEEE Transactions on Automatic Control, vol. 42, no. 1, pp. 101-105, 1997. · Zbl 0871.93045 · doi:10.1109/9.553692
[6] Y. Niu, J. Lam, et al., “Adaptive control using backing and neural networks,” Journal of Dynamic Systems, Measurement, and Control, vol. 127, pp. 313-526, 20052005.
[7] T. P. Zhang and 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. · Zbl 1282.93152 · doi:10.1016/j.automatica.2006.12.014
[8] Z. Wang, Y. Liu, and X. Liu, “On global asymptotic stability of neural networks with discrete and distributed delays,” Physics Letters A, vol. 345, pp. 299-308, 2005. · Zbl 1345.92017
[9] S. Xu, J. Lam, D. W. C. Ho, and Y. Zou, “.Improved global robust asymptotic stability criteria for delayed cellualar neural networks,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 35, pp. 1317-1321, 2005.
[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. · Zbl 1023.93056 · doi:10.1109/9.935057
[11] Q. Zhu, S. m. Fei, T. P. Zhang, and T. Li, “Control for a class of time-delay nonlinear systems,” Neurocomputing. In press. · doi:10.10161j.neucom.2008.04.012
[12] B. G. Xu and Y. Q. Liu, “An improved Razumikhin-type theorem and its applications,” IEEE Transactions on Automatic Control, vol. 39, no. 4, pp. 839-841, 1994. · Zbl 0825.93642 · doi:10.1109/9.286265
[13] S. Xu, J. Lam, and Y. Zou, “New results on delay-dependent robust H\infty control for systems with time-varying delays,” Automatica, vol. 42, no. 2, pp. 343-348, 2006. · Zbl 1099.93010 · doi:10.1016/j.automatica.2005.09.013
[14] R. M. Sanner and J. E. Slotine, “Gaussian networks for direct adaptive control,” IEEE Transactions on Networks Neural, Networks Neural, vol. 3, no. 6, pp. 837-863, 1992.
[15] F. Hong, S. Zhi, S. Ge, and T. H. Lee, “Practical adaptive Neural Control of Nonlinear systems with unknown time delays,” IEEE Transactions on Systems, vol. 35, no. 4, pp. 849-854, 2005.
[16] H. Wu, “Adaptive stabilizing state feedback controllers of uncertain dynamical systems with multiple time delays,” IEEE Transactions on Automatic Control, vol. 45, no. 9, pp. 1697-1701, 2000. · Zbl 0990.93119 · doi:10.1109/9.880623
[17] D. Yue and Q.-L. Han, “Delayed feedback control of uncertain systems with time-varying input delay,” Automatica, vol. 41, no. 2, pp. 233-240, 2005. · Zbl 1072.93023 · doi:10.1016/j.automatica.2004.09.006
[18] L. Dugard and E. I. Verriest, Stability and Control of Time-Delay Systems, vol. 228, Springer, London, UK, 1998. · Zbl 0901.00019 · doi:10.1007/BFb0027478
[19] Q. Zhu, S. m. Fei, T. P. Zhang, and T. Li, “Control for a class of time-delay nonlinear systems,” Neuro Computing. In press. · doi:10.10161j.neucom.2008.04.012
[20] V. B. Kolmanovskii, “Delay effects on stability,” in Asurvey Proceedings of 38th The CDC, pp. 1993-1998, 1999.
[21] S. K. Nguang, “Robust stabilization of a class of time-delay nonlinear systems,” IEEE Transactions on Automatic Control, vol. 45, no. 4, pp. 756-762, 2000. · Zbl 0978.93067 · doi:10.1109/9.847117
[22] S. Zhou, G. Feng, and S. K. Nguang, “Robust stabilization of a class of time-delay nonlinear systems,” IEEE Transactions on Automatic Control, vol. 47, no. 9, p. 1586, 2002. · Zbl 1364.93725 · doi:10.1109/TAC.2002.802754
[23] S. S. Ge, F. Hong, and T. H. Lee, “Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 34, pp. 499-516, 2004.
[24] Q. Zhu, et al., “Adaptive tracking control for input delayed MIMO nonlinear systems,” Neurocomputing, vol. 74, no. 1-3, pp. 472-480, 2010. · doi:10.1061j.neucom.2010.03.003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.