The concept of complete switched generalized function projective synchronization (CSGFPS) in practical type is introduced and the CSGFPS of a class of hyperchaotic systems with unknown parameters and disturbance inputs are investigated. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the states of a class of hyperchaotic systems asymptotically synchronized up to a desired scaling function and the unknown parameters are also estimated. In numerical simulations, the scaling function factors discussed in this paper are more complicated. Finally, the hyperchaotic Lorenz and hyperchaotic Lü systems are taken, for example, and the numerical simulations are presented to verify the effectiveness and robustness of the proposed control scheme.

References

References
1.
Yang
,
Y.
, and
Chen
,
Y.
,
2009
, “
The Generalized QS Synchronization Between the Generalized Lorenz Canonical Form and the Rossler System
,”
Chaos, Solitons Fractals
,
39
(
5
), pp.
2378
2385
.10.1016/j.chaos.2007.07.003
2.
Yu
,
F.
,
Wang
,
C.
,
Hu
,
Y.
, and
Yin
,
J.
,
2012
, “
Antisynchronization of a Novel Hyperchaotic System With Parameter Mismatch and External Disturbances
,”
Pramana, J. Phys.
,
79
(
1
), pp.
81
93
.10.1007/s12043-012-0285-6
3.
Zhang
,
Q.
,
Jinhu
,
L.
, and
Chen
,
S.
,
2010
, “
Coexistence of Antiphase and Complete Synchronization in the Generalized Lorenz System
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
(
10
), pp.
3067
3072
.10.1016/j.cnsns.2009.11.020
4.
Yu
,
F.
,
Wang
,
C.
,
Hu
,
Y.
, and
Yin
,
J.
,
2012
, “
Projective Synchronization of a Five-Term Hyperbolic-Type Chaotic System With Fully Uncertain Parameters
,”
Acta Phys. Sin.
,
61
(
6
), p.
060505
.10.7498/aps.61.060505
5.
Wang
,
B.
,
Shi
,
P.
,
Hamid
,
R. K.
, and
Wang
,
J.
,
2013
, “
Robust H∞ Synchronization of a Hyper-Chaotic System With Disturbance Input
,”
Nonlinear Anal.: Real World Appl.
,
14
(
3
), pp.
1487
1495
.10.1016/j.nonrwa.2012.10.011
6.
Wu
,
Z.
,
Shi
,
P.
,
Su
,
H.
, and
Chu
,
J.
,
2013
, “
Stochastic Synchronization of Markovian Jump Neural Networks With Time-Varying Delay Using Sampled-Data
,”
IEEE Trans. Cybern.
,
PP
(99), pp.
1
15
. 10.1109/TSMCB.2012.2230441
7.
Wu
,
Z.
,
Shi
,
P.
,
Su
,
H.
, and
Chu
,
J.
,
2013
, “
Sampled-Data Fuzzy Control of Chaotic Systems Based on t-s Fuzzy Model
,”
IEEE Trans. Fuzzy Syst.
,
PP
(99), p.
1
.10.1109/TFUZZ.2013.2249520
8.
Hamiche
,
H.
,
Kemih
,
K.
,
Ghanes
,
M.
,
Zhang
,
G.
, and
Djennoune
,
S.
,
2011
, “
Passive and Impulsive Synchronization of a New Four-Dimensional Chaotic System
,”
Nonlinear Anal. Theory, Methods Appl.
,
74
(
4
), pp.
1146
1154
.10.1016/j.na.2010.09.051
9.
Li
,
X.
, and
Rakkiyappan
,
R.
,
2013
, “
Impulsive Controller Design for Exponential Synchronization of Chaotic Neural Networks With Mixed Delays
,”
Commun. Nonlinear Sci. Numer. Simul.
,
18
(
6
), pp.
1515
1523
.10.1016/j.cnsns.2012.08.032
10.
Lin
,
C.
,
Peng
,
Y.
, and
Lin
,
M.
,
2009
, “
CMAC-Based Adaptive Backstepping Synchronization of Uncertain Chaotic Systems
,”
Chaos, Solitons Fractals
,
42
(
2
), pp.
981
988
.10.1016/j.chaos.2009.02.028
11.
Mainieri
,
R.
, and
Rehacek
,
J.
,
1999
, “
Projective Synchronization in Three-Dimensional Chaotic Systems
,”
Phys. Rev. Lett.
,
15
(
15
), pp.
3042
3045
.10.1103/PhysRevLett.82.3042
12.
Sun
,
Y.
,
Li
,
J.
,
Wang
,
J.
, and
Wang
,
H.
,
2010
, “
Generalized Projective Synchronization of Chaotic Systems via Adaptive Learning Control
,”
Chin. Phys. B
,
19
(
2
), p.
020505
.10.1088/1674-1056/19/2/020505
13.
Wang
,
X.
, and
Fan
,
B.
,
2012
, “
Generalized Projective Synchronization of a Class of Hyperchaotic Systems Based on State Observer
,”
Commun. Nonlinear Sci. Numer. Simul.
,
17
(
2
), pp.
953
963
.10.1016/j.cnsns.2011.06.016
14.
Du
,
H.
,
Shi
,
P.
, and
Lu
,
N.
,
2013
, “
Function Projective Synchronization in Complex Dynamical Networks With Time Delay via Hybrid Feedback Control
,”
Nonlinear Anal.: Real World Appl.
,
14
(
2
), pp.
1182
1190
.10.1016/j.nonrwa.2012.09.009
15.
Fu
,
G.
,
2012
, “
Robust Adaptive Modified Function Projective Synchronization of Different Hyperchaotic Systems Subject to External Disturbance
,”
Commun. Nonlinear Sci. Numer. Simul.
,
17
(
6
), pp.
2602
2608
.10.1016/j.cnsns.2011.09.033
16.
Wu
,
X.
,
Wang
,
H.
, and
Lu
,
H.
,
2011
, “
Hyperchaotic Secure Communication via Generalized Function Projective Synchronization
,”
Nonlinear Anal.: Real World Appl.
,
12
(
2
), pp.
1288
1299
.10.1016/j.nonrwa.2010.09.026
17.
Li
,
Z.
, and
Zhao
,
X.
,
2011
, “
Generalized Function Projective Synchronization of Two Different Hyperchaotic Systems With Unknown Parameters
,”
Nonlinear Anal.: Real World Appl.
,
12
(
5
), pp.
2607
2615
.10.1016/j.nonrwa.2011.03.009
18.
Li
,
H.
, and
Li
,
C.
,
2012
, “
Switched Generalized Function Projective Synchronization of Two Identical/Different Hyperchaotic Systems With Uncertain Parameters
,”
Phys. Scr.
,
86
(
4
), p.
045008
.10.1088/0031-8949/86/04/045008
19.
Yu
,
F.
,
Wang
,
C.
,
Wan
,
Q.
, and
Hu
,
Y.
,
2013
, “
Complete Switched Modified Function Projective Synchronization of a Five-Term Chaotic System With Uncertain Parameters and Disturbances
,”
Pramana, J. Phys.
,
80
(
2
), pp.
223
235
.10.1007/s12043-012-0481-4
20.
Wang
,
X.
, and
Wang
,
M.
,
2008
, “
A Hyperchaos Generated From Lorenz System
,”
Physica A
,
387
(
14
), pp.
3751
3758
.10.1016/j.physa.2008.02.020
21.
Pang
,
S.
, and
Liu
,
Y.
,
2011
, “
A New Hyperchaotic System From the Lü System and Its Control
,”
J. Comput. Appl. Math.
,
235
(
8
), pp.
2775
2789
.10.1016/j.cam.2010.11.029
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