An adaptive sliding mode control scheme for a class of chaotic systems with mismatched perturbations and input nonlinearities. (English) Zbl 1221.93050

Summary: We are concerned with the stabilization problem for a class of chaotic systems with mismatched perturbations and input nonlinearities. A novel sliding surface is specially designed so that when the system enters the sliding mode, the mismatched perturbations can be effectively overcome and achieve asymptotic stability. Then, an adaptive sliding mode controller (ASMC) is proposed to drive the controlled state trajectories into the designated sliding surface in finite time even subjected to input nonlinearities. Finally, the corresponding numerical simulations are demonstrated to verify the effectiveness of proposed method.


93B12 Variable structure systems
34H10 Chaos control for problems involving ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35 Dynamical systems in control
Full Text: DOI


[1] Ogorzalek, M. J., Chaos and complexity in nonlinear electronic circuits (1997), Word Scientific: Word Scientific Singapore · Zbl 0924.58053
[2] Yan, J. J., Controlling chaos of a chaotic nonlinear gyro using variable structure control, Mech Syst Signal Process, 21, 2515-2522 (2006)
[3] Chen, G.; Dong, X., From chaos to order: methodologies, perspective and applications (1998), World Scientific: World Scientific Singapore · Zbl 0908.93005
[4] Chen, M.; Zhou, D.; Shang, Y., A new observer-based synchronization scheme for private communication, Chaos, Soliton & Fractals, 24, 1025-1030 (2005) · Zbl 1069.94508
[5] Wang, H., Finite-time chaos control via nonsingular terminal sliding mode control, Commun Nonlinear Sci Numer Simulat, 14, 2728-2733 (2009) · Zbl 1221.37225
[6] Du, J. G.; Huang, T. W.; Sheng, Z. H., Analysis of decision-making in economic chaos control, Nonlinear Anal Real World Appl, 10, 2493-2501 (2009) · Zbl 1163.91331
[7] Cheng, C. C.; Wen, C. C.; Lee, W. T., Design of decentralised sliding surfaces for a class of large-scale systems with mismatched perturbations, Int J Control, 82, 2013-2025 (2009) · Zbl 1175.93007
[8] Chou, C. H.; Cheng, C. C., A decentralized model reference adaptive variable structure controller for large-scale time-varying delay systems, IEEE Trans Automat Control, 32, 1786-1790 (2007)
[9] Huang, C. F.; Cheng, K. H.; Yan, J. J., Robust chaos synchronization of four-dimensional energy resource systems subject to unmatched uncertainties, Commun Nonlinear Sci Numer Simulat, 14, 2784-2792 (2009)
[10] Wang, Y. Q.; Jiang, C. H.; Zhou, D. H.; Gao, F. R., Variable structure control for a class of nonlinear systems with mismatched uncertainties, Appl Math Comput, 200, 387-400 (2008) · Zbl 1146.93014
[11] Choi, H. H., Variable structure output feedback control design for a class of uncertain dynamic systems, Automatica, 38, 335-341 (2002) · Zbl 0991.93021
[12] Wang, H.; Han, Z. Z.; Xie, Q. Y.; Zhang, W., Sliding mode control for chaotic systems based on LMI, Commun Nonlinear Sci Numer Simulat, 14, 1410-1417 (2009) · Zbl 1221.93049
[13] Wen, C. C.; Cheng, C. C., Design of sliding surface for mismatched uncertain systems to achieve asymptotical stability, J Franklin Inst, 345, 926-941 (2008) · Zbl 1201.93108
[14] Leon, S. J., Linear algebra with applications (1999), Prentice-Hall: Prentice-Hall New Jersey
[15] Tao, G., Adaptive control design and analysis (2003), John Wiley: John Wiley New Jersey · Zbl 1061.93004
[16] Corradini, M. L.; Orlando, G., Linear unstable plants with saturating actuators: robust stabilization by a time varying sliding surface, Automatica, 43, 88-94 (2007) · Zbl 1140.93467
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