Chaos control in delayed chaotic systems via sliding mode based delayed feedback.

*(English)*Zbl 1197.34112Summary: This paper investigates chaos control for scalar delayed chaotic systems using sliding mode control strategy. Sliding surface design is based on delayed feedback controller. It is shown that the proposed controller can achieve stability for an arbitrary unstable fixed point (UPF) or unstable periodic orbit (UPO) with arbitrary period. The chaotic system used in this study to illustrate the theoretical concepts is the well known Mackey-Glass model. Simulation results show the effectiveness of the designed nonlinear sliding mode controller.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

##### MSC:

34H10 | Chaos control for problems involving ordinary differential equations |

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\textit{N. Vasegh} and \textit{A. K. Sedigh}, Chaos Solitons Fractals 40, No. 1, 159--165 (2009; Zbl 1197.34112)

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##### References:

[1] | Mackey, M.C.; Glass, L., Oscillation and chaos on physiological control systems, Science, 197, 287-289, (1977) · Zbl 1383.92036 |

[2] | Farmer, J.D., Chaotic attractor of an infinite dimensional dynamical system, Phys D, 4, 3, 366-393, (1982) · Zbl 1194.37052 |

[3] | Fowler, A.C.; Kember, G., Delay recognition in chaotic time series, Phys lett A, 175, 402-408, (1993) |

[4] | Lu, H.; He, Z., Chaotic behaviors in first-order autonomous continuous-time systems with delay, IEEE trans CAS I, 43, 8, 700-702, (1996) |

[5] | Tian, Y.-C.; Gao, F., Adaptive control of chaotic continuous-time systems with delay, Phys D, 117, 1-12, (1998) · Zbl 0941.93534 |

[6] | Ott, E.; Grebogi, C.; Yorke, J.A., Controlling chaos, Phys rev lett, 64, 1196-1199, (1990) · Zbl 0964.37501 |

[7] | Senesac, L.R.; Blass, W.E.; Chin, G., Controlling chaotic systems with occasional proportional feedback, Rev sci instr, 70, 1719-1724, (1999) |

[8] | Pyragas, K., Continuous control of chaos by self-controlling feedback, Phys lett A, 170, 421-428, (1992) |

[9] | Park, J.H.; Kwon, O.M., A novel criterion for delayed feedback control of time-delay chaotic systems, Chaos solitons & fractals, 23, 495-501, (2005) · Zbl 1061.93507 |

[10] | Song, Y.; Wei, J., Bifurcation analysis for chen’s system with delayed feedback and its application to control of chaos, Chaos solitons & fractals, 22, 75-91, (2004) · Zbl 1112.37303 |

[11] | Weihua, J.; Junjie, W., Bifurcation analysis in a limit cycle oscillator with delayed feedback, Chaos solitons & fractals, 23, 817-831, (2005) · Zbl 1080.34054 |

[12] | Itkis, U., Control system of variable structure, (1976), Wiley NewYork |

[13] | Utkin, V.I., Sliding mode and their application in variable structure systems, (1978), Mir Editors Moscow · Zbl 0398.93003 |

[14] | Slotine, J.J.E.; Li, W., Applied nonlinear control, (1991), Prentice Hall |

[15] | Nazzal, J.M.; Natsheh, A.N., Chaos control using sliding-mode theory, Chaos solitons & fractals, 33, 695-702, (2007) |

[16] | Yau, H.T.; Yan, J.J., Robust controlling hyperchaos of Rössler system subject to input nonlinearity by using sliding mode control, Chaos solitons & fractals, 33, 1767-1776, (2007) · Zbl 1136.93438 |

[17] | Pyragas, K., Control of chaos via an unstable delayed feedback controller, Phys rev lett, 86, 2265-2268, (2001) |

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