Abstract
In this paper a robust intelligent RBF neural network tracking control system combined with a distance-based sliding-mode control technique is proposed for a class of chaos systems. The proposed adaptive control scheme is developed for a class of chaotic systems with unknown bounded uncertainties. The adaptation laws are derived using a Lyapunov stability analysis, so that both system tracking stability and error convergence can be guaranteed in the closed-loop system. It is used to demonstrate the effectiveness and performance of the proposed robust control technique.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Li, Z., Han, C., Shi, S.: Modification for synchronization of Rossler and Chen chaotic systems. Physics Letters A 301(3-4), 224–230 (2002)
Cao, J., Li, H.X., Ho, W.C.: Synchronization criteria of Lur’e systems with time-delay feedback control. Chaos, Solitons & Fractals 23(4), 1285–1298 (2005)
Kakmeni, F.M.M., Bowong, S., Tchawoua, C.: Reduced-order synchronization of uncertain chaotic systems via adaptive control. Communications in Nonlinear Science and Numerical Simulation 11(7), 810–830 (2006)
Wang, C.C., Su, J.P.: A novel variable structure control scheme for chaotic synchronization. Chaos, Solitons & Fractals 18(2), 275–287 (2003)
Huang, L., Wang, M., Feng, R.: Synchronization of generalized Henon map via backstepping design. Chaos, Solitons & Fractals 23(2), 617–620 (2005)
Cao, J., Li, H.X., Ho, W.C.: Synchronization criteria of Luynchronization of Rossler and Chen chaotic dynamical systems using active control. Physics Letters A 278(4), 191–197 (2001)
Wang, Y., Guan, Z.H., Wen, X.: Adaptive synchronization for Chen chaotic system with fully unknown parameters. Chaos, Solitons & Fractals 19(4), 899–903 (2004)
Zhang, H., Ma, X.K.: Synchronization of uncertain chaotic systems with parameters perturbation via active control. Chaos, Solitons & Fractals 21(1), 39–47 (2004)
Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Physical Review Letters 64(8), 821–825 (1990)
Behera, L., Gopal, M., Chaudhury, S.: Inversion of RBF networks and applications to adaptive control of nonlinear systems. IEE Proceedings of Control Theory and Applications 142(6), 617–624 (1995)
Li, Y., Qiang, S., Zhuang, X., Kaynak, O.: Robust and adaptive backstepping control for nonlinear systems using RBF neural networks. IEEE Trans. on Neural Networks 15(3) (2006)
Peng, H.T., Ozaki, H., Ozaki, V.T.: A parameter optimization method for radial basis function type models. IEEE Trans. on Neural Networks 14(2), 432–438 (2003)
Lian, J., Lee, Y., Zak, S.H.: Variable neural direct adaptive robust control of uncertain systems. IEEE Trans. on Automatic Control 53(11), 2658–2664 (2008)
Feng, J., Ng, K.T.: An adaptive demodulator for the chaotic modulation communication system with RBF neural network: Chow, Circuits and Systems I. IEEE Trans. on Fundamental Theory and Applications 47(6), 902–909 (2000)
Leung, H., Hennessey, G., Drosopoulos, A.: Signal detection using the radial basis function coupled map lattice. IEEE Trans. on Neural Networks 11(5), 1133–1151 (2000)
Muller, A., Elmirghani, J.M.H.: Novel approaches to signal transmission based on chaotic signals and artificial neural networks. IEEE Trans. on Communications 50(3), 384–390 (2002)
Choi, B.J., Kwak, S.W., Kim, B.K.: Design of a single-input fuzzy logic controller and its properties. Fuzzy Sets and Syst. 106(3), 299–308 (1999)
Choi, B.J., Kwak, S.W., Kim, B.K.: Design and stability analysis of single-input fuzzy logic controller. IEEE Trans. on Systems, Man and Cyber., Part B 30(2), 303–309 (2000)
Jamal, M.N., Ammar, N.N.: Chaos control using sliding-mode theory. Chaos, Solitons & Fractals 33(2), 695–702 (2007)
Ablay, G.: Sliding mode control of uncertain unified chaotic systems: nonlinear analysis. Hybrid Systems 3(4), 531–535 (2009)
Yau, H.T.: Design of adaptive sliding mode controller for chaos synchronization with uncertainties. Chaos, Solitons & Fractals 22(2), 341–347 (2004)
Konishi, K., Hirai, M., Kokame, H.: Sliding mode control for a class of chaotic systems. Physics Letters A 245(6), 511–517 (1998)
Lu, Z., Shieh, L., Chen, S.G., Coleman, N.P.: Simplex sliding mode control for nonlinear uncertain systems via chaos optimization. Chaos, Solitons & Fractals 23(3), 747–755 (2005)
Chang, J.F., Hung, M.L., Yang, Y.S., Liao, T.L., Yan, J.J.: Controlling chaos of the family of Rössler systems using sliding mode control. Chaos, Solitons & Fractals 37(2), 609–622 (2008)
Guo, H., Lin, S., Liu, J.: A radial basis function sliding mode controller for chaotic Lorenz system. Physics Letters A 351(4-5), 257–261 (2006)
Jianjun, N., Yongling, F., Xiaoye, Q.: Design and application of discrete sliding mode control with RBF network-based switching Law. Chinese Journal of Aeronautics 22(3), 279–284 (2009)
Selami, B., Musa, A.: Stable modeling based control methods using a new RBF network. ISA Transactions 49(4), 510–518 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, YC., Hung, LC., Chao, SH. (2011). RBF Network with Sliding-Mode Control for Chaos Systems. In: Tan, H., Zhou, M. (eds) Advances in Information Technology and Education. Communications in Computer and Information Science, vol 201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22418-8_37
Download citation
DOI: https://doi.org/10.1007/978-3-642-22418-8_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22417-1
Online ISBN: 978-3-642-22418-8
eBook Packages: Computer ScienceComputer Science (R0)