This paper investigates the control of a class of four-dimensional chaotic systems with system parameters varying randomly under the condition of noise. Based on the sliding mode control method, the controller is designed to eliminate the chaotic behavior of a system and realize its stabilization. Numerical simulations are presented to demonstrate the validity of the proposed method. The approach proposed in this paper is simple and easy to implement and also provides reference for chaos control in relevant systems.
AtaeiMHaghighatdarF (2011) Adaptive nonlinear feedback design for chaos suppression and regulation in uncertain unified chaotic system. International Journal of Innovative Computing Information and Control. 7(5A): 2051–2062.
2.
BashkirtsevaIRyashkoL (2011) Control of equilibria for nonlinear stochastic discrete-time systems. IEEE Transactions on Automatic Control. 56(9): 2162–2166.
3.
CaiCHXuZYXuWBFengB (2002) Notch filter feedback control in a class of chaotic systems. Automatica. 38(4): 695–701.
4.
ChenDYLiuYXMaXYZhangRF (2012) Control of a class of fractional-order chaotic systems via sliding mode. Nonlinear Dynamics. 67(1): 893–901.
5.
ChenDYShenTMaXY (2011a) Sliding mode control of chaotic vibrations of spinning disks with uncertain parameter under bounded disturbance. Acta Physica Sinica. 60(5): 050505 [in Chinese]–050505 [in Chinese].
6.
ChenDYZhaoWLMaXYZhangRF (2011) No-chattering sliding mode control chaos in Hindmarsh-Rose neurons with uncertain parameters. Computers & Mathematics with Applications. 61(10): 3161–3171.
7.
Chen DY, Zhang RF, Ma XY and Liu S (2011b) Chaotic synchronization and anti-synchronization for a novel class of multiple chaotic systems via a sliding mode control scheme. Nonlinear Dynamics. Epub ahead of print 1 December 2011. DOI: 10.1007/s11071-011-0244-7.
8.
ChenG (2011) A simple adaptive feedback control method for chaos and hyper-chaos control. Applied Mathematics and Coputation. 217(17): 7258–7264.
9.
De PaulaASSaviMA (2009) A multiparameter chaos control method based on OGY approach. Chaos Solitons & Fractals. 40(3): 1376–1390.
10.
HuaCGuanXLiXShiP (2004) Adaptive observer-based control for a class of chaotic systems. Chaos, Solitions & Fractals. 22: 103–110.
11.
HuaCGuanXShiP (2005) Adaptive feedback control for a class of chaotic systems. Chaos, Solitons and Fractals. 23(3): 757–765.
12.
LiHYHuYA (2011) Robust sliding-mode backstepping design for synchronization control of cross-strict feedback hyperchaotic systems with unmatched uncertainties. Communications in Nonlinear Science and Numerical Simulation. 16(10): 3904–3913.
13.
LinTCLeeTY (2011) Chaos synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive fuzzy sliding mode control. IEEE Transcations on Fuzzy systems. 19(4): 623–635.
14.
LinTCLeeTYBalasVE (2011) Adaptive fuzzy sliding mode control for synchronization of uncertain fractional order chaotic systems. Chaos Solitons & Fractals. 44(10): 791–801.
15.
LiuYYangQ (2010) Dynamics of a new Lorenz-like chaotic system. Nonlinear Analysis: Real World Applications. 11(4): 2563–2572.
16.
LuJHChenGR (2005) A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Transactions on Automatic Control. 50(6): 841–846.
17.
Mahmoud GamalMAhmedME (2011) Modified projective synchronization and control of complex Chen and Lu systems. Journal of Vibration and Control. 17(8): 1184–1194.
18.
NjahAN (2010) Tracking control and synchronization of the new hyperchaotic Liu system via backstepping techniques. Nonlinear Dynamics. 61(1−2): 1–9.
19.
RahmaniZMotlaghMRJDittoW (2009) Robust control of spatiotemporal chaos in coupled map lattices. International Journal of Bifurcation and Chaos. 19(6): 2031–2042.
20.
RenHPLiuD (2006) Nonlinear feedback control of chaos in permanent magnet synchronous motor. IEEE Transactions on Circuits and Systems I–Express Briefs. 53(1): 45–50.
21.
SahabARZiabariMTAlamdariSAS (2010) Chaos control via optimal generalized backstepping method. International Review of Electrical Engineering. 5(5): 2129–2140.
22.
SchiffSJJergerKDuongDH (1994) Controlling chaos in the brain. Nature. 370(6491): 615–620.
23.
SoundarrajanASumathiS (2011) Fuzzy-based intelligent controller for power generating systems. Journal of Vibration and Control. 17(8): 1265–1278.
24.
SprottJC (2011) A new chaotic Jerk circuit. IEEE Transactions on Circuits and Systems II-Express Briefs. 58(4): 240–243.
25.
SunGHWangMWuLG (2011) Unexpected results of extended fractional Kalman filter for parameter identification in fractional order chaotic systems. International Journal of Innovative Computing, Information and Control. 7(9): 5341–5352.
26.
WangLDTangSChuZY (2010) Recurrence and distribution chaotic in coupled map lattices. Innovative Computing, Information and Control Express Letters. 4(1): 19–24.
27.
WangWXYangRLaiYCKovanisVGrebogiC (2011) Predicting catastrophes in nonlinear dynamical systems by compressive sensing. Physical Review Letters. 106: 154101–154101.
XiangWHuangpuYG (2010) Sliding mode control for a new hyperchaotic dynamical system. Innovative Computing, Information and Control Express Letters. 4(2): 547–552.
30.
YinYYLiuFShiP (2010) Finite-time continous gain-scheduled control on stochastic hyperchaotic systems. Proceedings of the Institution of Mechanical Engineering Part I – Journal of Systems and Control Engineering. 224(16): 679–688.
31.
YoshimuraT (2011) Discrete-time adaptive sliding mode control for a class of uncertain time delay systems. Journal of Vibration and Control. 17(7): 1009–1020.
32.
YuJChenBYuH (2011) Adaptive fuzzy tracking control for the chaotic permanent magnet synchronous motor drive system via backstepping. Nonlinear Analysis – Real World Applications. 12(1): 671–681.
33.
ZhaoZJiaMXWangFLWangS (2009) Intermittent chaos and sliding window symbol sequence statistics-based early fault diagnosis for hydraulic pump on hydraulic tube tester. Mechanical Systems and Signal Processing. 23(5): 1573–1585.
