In this paper, a projective synchronization problem of master-slave chaotic systems is investigated. More specifically, a fuzzy adaptive slave chaotic system subject to both sector nonlinearities and dead-zone in the input channel is proposed using only the measurable output of the master system thanks to a suitable observer. The asymptotical projective synchronization between the master and slave systems is achieved by an adequate fuzzy adaptive variable-structure control system. The underlying parameter adaptation design as well as the asymptotical synchronization and stability analysis are carried out using a Lyapunov based approach. The distinctive feature of the control design is that the uncertainties function and the gain reduction tolerances of the dead-zone are no longer required to be known thanks to the parameter adaptation capability of the control system. The proposed synchronization scheme is extended to two classes of the master-slave chaotic systems with time-delays. By using the Lyapunov-Krasovskii approach, some stability conditions relating to these classes are derived. Simulation results are given to show the effectiveness of the proposed projective synchronization scheme.
BoulkrouneAChekirebHTadjineMBouatmaneS (2006a) Observer-based adaptive feedback controller of a class of chaotic systems. International Journal of Bifurcation and Chaos16: 189–196.
2.
BoulkrouneAChekirebHTadjineMM’SaadM (2006b) Fuzzy adaptive controller based on observers for a class of unknown chaotic systems in Proceedings of the first IFAC Conference on Analysis and Control of Chaotic Systems. Reims, France, June 28–30, pp. 25–30.
3.
BoulkrouneAChekirebHTadjineMBouatmaneS (2007) An adaptive feedback controller with observer for linearizable chaotic systems. Control and Intelligent Systems35: 1–8.
4.
BoulkrouneATadjineMM’saadMFarzaM (2008) How to design a fuzzy adaptive control based on observers for uncertain affine nonlinear systems. Fuzzy Sets and Systems159: 926–948.
5.
BoulkrouneATadjineMM’saadMFarzaM (2009) Adaptive fuzzy controller for non-affine systems with zero dynamics. International Journal of Systems Science40: 367–382.
6.
BowongaSKakmenibMKoinacR (2006) Chaos synchronization and duration time of a class of uncertain systems. Mathematics and Computers in Simulation71: 212–228.
7.
CailianCGangFXinpingG (2005) An adaptive lag-synchronization method for time-delay chaotic systems,. in Proceedings of the American Control Conference, Portland, OR, USA, June 8–10, pp. 4277-4282.
ChenCYLinJWLeeWIChenCW (2010) Fuzzy control for an oceanic structure: A case study in time-delay TLP system. Journal of Vibration and Control16: 147–160.
10.
ChenGDongX (1998) From Chaos to Order: Methodologies Perspectives and Applications, Singapore: World-Scientific.
11.
HungYCHwangCCLiaoTL (2006) Generalized projection synchronization of chaotic systems with unknown dead-zone input: Observer-based approach. Chaos16: 033125.
12.
HungYCYanJJLiaoTL (2008) Projection synchronization of Chua's chaotic systems with dead-zone in the control input. Mathematics and Computers in Simulation77: 374–382.
13.
HwangEJHyunCHKimEParkM (2009) Fuzzy model based adaptive synchronization of uncertain chaotic systems: Robust tracking control approach. Physics Letters A373: 1935–1939.
JianpingYChangpinL (2005) Generalized projective synchronization of a unified chaotic system. Chaos Solitons and Fractals26: 1119–1124.
16.
KungCCChenTH (2006) Adaptive fuzzy controller design for time-delay systems with input containing sector nonlinearities and dead-zone in Proceedings of the IEEE International Conference on Fuzzy Systems. Vancouver, BC, Canada, July 16–21, pp. 463–467.
17.
KungCCChangSCChenYR (2008) Observer-based robust adaptive fuzzy sliding mode control for unknown nonlinear dynamical systems with dead-zone input in Proceedings of the IEEE International Conference on Systems Man and Cybernetics Suntec, Singapore, 12–15 Oct., pp. 950–955.
18.
LiG (2006) Projective synchronization of chaotic system using backstepping control. Chaos Solitons and Fractals29: 490–598.
19.
LiZXuD (2004) A secure communication scheme using projective chaos synchronization. Chaos Solitons and Fractals22: 477–484.
20.
LiaoTLHuangNS (1999) An observer-based approach for chaotic synchronization with applications to secure communications. IEEE Transactions on Circuits and Systems I46: 1144–1150.
21.
LiuY-JWangW (2007) Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems. Information Sciences177: 3901–3917.
22.
LiuY-JZhengYQ (2009) Adaptive robust fuzzy control for a class of uncertain chaotic systems. Nonlinear Dynamics57: 431–439.
23.
LiuY-JWangWWTongSLiuY-S (2010) Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters. IEEE Transactions on Systems Man and Cybernetics Part A: Systems and Humans40: 170–184.
MorgulOSolakE (1997) On the synchronization of chaotic systems by using state observers. International Journal of Bifurcation and Chaos7: 1307–1322.
26.
PecoraLMCarrollTL (1990) Synchronization in chaotic systems. Physic Review Letters64: 821–824.
27.
PikovskyASRosenblumMGOsipovGVKurthsJ (1997) Phase synchronization of chaotic oscillators by external driving. Physica D104: 219–238.
28.
PoursamadAMarkaziAHD (2009) Adaptive fuzzy sliding-mode control for multi-input multi-output chaotic systems. Chaos Solitons and Fractals42: 3100–3109.
29.
RoopaeiMZolghadriJJahromiM (2008) Synchronization of two different chaotic systems using novel adaptive fuzzy sliding mode control. Chaos18: 033133–033133.
SolihinMIWahyudiJLegowoA (2010) Fuzzy-tuned PID anti-swing control of automatic gantry crane. Journal of Vibration and Control16: 127–145.
33.
SunJZhangY (2004) Impulsive control and synchronization of Chua's oscillators. Mathematics and Computers in Simulation66: 499–508.
34.
TongSLiH-H (2002) Observer-based robust fuzzy control of nonlinear systems with parametric uncertainties. Fuzzy Sets and Systems131: 165–184.
35.
TussetAMRafikovMBalthazarJM (2009) An intelligent controller design for magnetorheological damper based on a quarter-car model. Journal of Vibration and Control15: 1907–1920.
36.
WangLX (1994) Adaptive Fuzzy Systems and Control: Design and Stability Analysis, Englewood Cliffs, NJ: Prentice-Hall.
37.
WenGXuD (2004) Observer-based control for full-state projective synchronization of a general class of chaotic maps in any dimension. Physics Letters A333: 420–425.
38.
WenGXuD (2005) Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems. Chaos Solitons and Fractals26: 71–77.
39.
YuXSongY (2001) Chaos synchronization via controlling partial state of chaotic systems. International Journal of Bifurcation and Chaos11: 1737–1741.
40.
ZhangHBienZ (2000) Adaptive fuzzy control of MIMO nonlinear systems. Fuzzy Sets and Systems115: 191–204.
41.
ZhangHCaiLBienZ (2000) A fuzzy basis function vector-based multivariable adaptive fuzzy controller for nonlinear systems. IEEE Transactions on Systems Man and Cybernetics Part B30: 210–217.
