This paper presents an adaptive robust controller for a class of uncertain chaotic Rossler system with time-varying mismatched parameters. The proposed controller is designed based on Lyapunov stability theory, and it is shown that using this controller all signals of the closed-loop system are uniformly ultimately bounded (UUB). In addition, the proposed scheme is such that it does not require a priori information about the bound of uncertainties. Furthermore, since all the signals are UUB, the control signal is smooth and feasible to implement. Simulation results on a third-order Rossler system with time-varying parameters confirm the effectiveness of the proposed controller.
Issue Section:
Research Papers
References
1.
Ott
, E.
, Grebogi
, C.
, and Yorke
, J. A.
, 1990
, “Controlling Chaos
,” Phys. Rev. Lett.
, 64
(11
), pp. 1196
–1199
.2.
Wang
, X.
, and Wang
, M.
, 2008
, “A Hyperchaos Generated From Lorenz System
,” Physica A
, 387
(14
), pp. 3751
–3758
.3.
Dou
, F. Q.
, Sun
, J. A.
, Duan
, W. S.
, and Lü
, K. P.
, 2009
, “Controlling Hyperchaos in the New Hyperchaotic System
,” Commun. Nonlinear Sci. Numer. Simul.
, 14
(2
), pp. 552
–559
.4.
Arefi
, M.
, and Jahed-Motlagh
, M.
, 2012
, “Robust Synchronization of Rossler Systems With Mismatched Time-Varying Parameters
,” Nonlinear Dyn.
, 67
(2
), pp. 1233
–1245
.5.
Hai
, M. J.
, and Ling
, M. L.
, 2008
, “Improved Piece-Wise Linear and Nonlinear Synchronization of a Class of Discrete Chaotic Systems
,” Int. J. Comput. Math.
, 87
(3
), pp. 619
–628
.6.
Park
, J. H.
, and Kwon
, O. M.
, 2005
, “A Novel Criterion for Delayed Feedback Control of Time-Delay Chaotic Systems
,” Chaos, Solitons Fractals
, 23
(2
), pp. 495
–501
.7.
Zhang
, H.
, Ma
, X.-K.
, Li
, M.
, and Zou
, J.-L.
, 2005
, “Controlling and Tracking Hyperchaotic Rössler System Via Active Backstepping Design
,” Chaos, Solitons Fractals
, 26
(2
), pp. 353
–361
.8.
Yu-Ping
, T.
, and Yu
, X.
, 2000
, “Adaptive Control of Chaotic Dynamical Systems Using Invariant Manifold Approach
,” IEEE Trans. Circuits Syst. I
, 47
(10
), pp. 1537
–1542
.9.
Ansari
, S. P.
, and Das
, S.
, 2014
, “Projective Synchronization of Time-Delayed Chaotic Systems With Unknown Parameters Using Adaptive Control Method
,” Math. Methods Appl. Sci.
, 38
(4
), pp. 726
–737
.10.
Arefi
, M. M.
, and Jahed-Motlagh
, M. R.
, 2010
, “Adaptive Robust Synchronization of Rossler Systems in the Presence of Unknown Matched Time-Varying Parameters
,” Commun. Nonlinear Sci. Numer. Simul.
, 15
(12
), pp. 4149
–4157
.11.
Arefi
, M. M.
, and Jahed-Motlagh
, M. R.
, 2009
, “Adaptive Robust Control of Hyperchaotic Rossler System in the Presence of Matching Disturbance
,” Second IFAC Meeting Related to Analysis and Control of Chaotic Systems
, Queen Mary University, London.12.
Osipov
, G.
, Glatz
, L.
, and Troger
, H.
, 1998
, “Suppressing Chaos in the Duffing Oscillator by Impulsive Actions
,” Chaos, Solitons Fractals
, 9
(1–2
), pp. 307
–321
.13.
Jang
, M.-J.
, Chen
, C.-L.
, and Chen
, C.-K.
, 2002
, “Sliding Mode Control of Hyperchaos in Rössler Systems
,” Chaos, Solitons Fractals
, 14
(9
), pp. 1465
–1476
.14.
Yau
, H.-T.
, and Yan
, J.-J.
, 2007
, “Robust Controlling Hyperchaos of the Rössler System Subject to Input Nonlinearities by Using Sliding Mode Control
,” Chaos, Solitons Fractals
, 33
(5
), pp. 1767
–1776
.15.
Zhang
, Q.
, 2014
, “Robust Synchronization of FitzHugh–Nagumo Network With Parameter Disturbances by Sliding Mode Control
,” Chaos, Solitons Fractals
, 58
, pp. 22
–26
.16.
Yan
, J.-J.
, 2004
, “H∞ Controlling Hyperchaos of the Rössler System With Input Nonlinearity
,” Chaos, Solitons Fractals
, 21
(2
), pp. 283
–293
.17.
Zhao
, M.
, and Wang
, J.
, 2014
, “Control of a Chaotic Finance System in the Presence of External Disturbance and Input Time-Delay
,” Appl. Math. Comput.
, 233
, pp. 320
–327
.18.
Femat
, R.
, 2002
, “An Extension to Chaos Control Via Lie Derivatives: Fully Linearizable Systems
,” Chaos
, 12
(4
), pp. 1027
–1033
.19.
Lin
, D.
, and Wang
, X.
, 2011
, “Self-Organizing Adaptive Fuzzy Neural Control for the Synchronization of Uncertain Chaotic Systems With Random-Varying Parameters
,” Neurocomputing
, 74
(12–13
), pp. 2241
–2249
.20.
Lin
, D.
, and Wang
, X.
, 2010
, “Observer-Based Decentralized Fuzzy Neural Sliding Mode Control for Interconnected Unknown Chaotic Systems Via Network Structure Adaptation
,” Fuzzy Sets Syst.
, 161
(15
), pp. 2066
–2080
.21.
Lin
, D.
, Wang
, X.
, Nian
, F.
, and Zhang
, Y.
, 2010
, “Dynamic Fuzzy Neural Networks Modeling and Adaptive Backstepping Tracking Control of Uncertain Chaotic Systems
,” Neurocomputing
, 73
(16–18
), pp. 2873
–2881
.22.
Lazzouni
, S. A.
, Bowong
, S.
, Kakmeni
, F. M. M.
, Cherki
, B.
, and Ghouali
, N.
, 2007
, “Chaos Control Using Small-Amplitude Damping Signals of the Extended Duffing Equation
,” Commun. Nonlinear Sci. Numer. Simul.
, 12
(5
), pp. 804
–813
.23.
Jin Yuan
, H.
, Chi Chuan
, H.
, An Pei
, W.
, and Li
, W. J.
, 1999
, “Controlling Hyperchaos of the Rossler System
,” Int. J. Control
, 72
(10
), pp. 882
–886
.24.
Li
, Z.
, Chen
, G.
, Shi
, S.
, and Han
, C.
, 2003
, “Robust Adaptive Tracking Control for a Class of Uncertain Chaotic Systems
,” Phys. Lett. A
, 310
(1
), pp. 40
–43
.25.
Estrada
, J. L.
, Duarte-Mermoud
, M. A.
, Travieso-Torres
, J. C.
, and Beltran
, N. H.
, 2008
, “Simplified Robust Adaptive Control of a Class of Time-Varying Chaotic Systems
,” Int. J. Comput. Math. Electr. Electron. Eng.
, 27
(2
), pp. 511
–519
.26.
Duarte-Mermoud
, M. A.
, Estrada
, J. L.
, and Travieso-Torres
, J. C.
, 2009
, “Adaptive Stabilization of Linear and Nonlinear Plants in the Presence of Large and Arbitrarily Fast Variations of the Parameters
,” J. Franklin Inst.
, 346
(8
), pp. 752
–767
.27.
Qu
, Z.
, 1992
, “Global Stabilization of Nonlinear Systems With a Class of Unmatched Uncertainties
,” Syst. Control Lett.
, 18
(4
), pp. 301
–307
.28.
Arefi
, M.
, and Jahed-Motlagh
, M.
, 2012
, “Adaptive Robust Stabilization of a Class of Uncertain Non-Linear Systems With Mismatched Time-Varying Parameters
,” Proc. Inst. Mech. Eng., Part I
, 226
(2
), pp. 204
–214
.29.
Marino
, R.
, and Tomei
, P.
, 1995
, Nonlinear Control Design: Geometric, Adaptive and Robust
, Prentice Hall
, London
.30.
Isidori
, A.
, 1995
, Nonlinear Control Systems
, Springer Verlag
, Berlin
.31.
Khalil
, H. K.
, 2002
, Nonlinear Systems
, Printice Hall
, Upper Saddle River, NJ.Copyright © 2016 by ASME
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