In this work, we propose an adaptive node-to-node pinning control strategy. In this approach, both the coupling strength among nodes and the pinning control gains are adaptively changed according to well chosen adaptation laws that take into account the specificities of the oscillators and the network topology. Proof of stability and performance comparison is also shown in this paper.

1.
J.
Cortes
,
S.
Martinez
, and
F.
Bullo
,
IEEE Trans. Autom. Control
51
,
1289
(
2006
).
2.
D. A.
Paley
,
N. E.
Leonard
,
R.
Sepulchre
,
D.
Grunbaum
, and
J. K.
Parrish
,
IEEE Control Syst. Mag.
27
,
89
(
2007
).
3.
D. A.
Paley
,
N. E.
Leonard
, and
R.
Sepulchre
,
Syst. Control
57
,
209
(
2008
).
4.
F.
Sorrentino
and
E.
Ott
,
Phys. Rev. Lett
100
,
114101
(
2008
).
5.
A. B.
Cohen
,
B.
Ravoori
,
F.
Sorrentino
,
T. E.
Murphy
,
E.
Ott
, and
R.
Roy
,
Chaos
20
,
043142
(
2010
).
6.
N. E.
Leonard
and
E.
Fiorelli
, in Proceedings of the 40th IEEE Conference on Decision and Control 2001 (
IEEE
,
2001
), Vol.
3
, pp.
2968
2973
.
7.
R.
Olfati-Saber
and
R. M.
Murray
,
IEEE Trans. Autom. Control
49
(
9
),
1520
(
2004
).
8.
I. D.
Couzin
,
J.
Krause
,
N. R.
Franks
, and
S. A.
Levin
,
Nature
433
,
513
(
2005
).
9.
B.
Nabet
,
N. E.
Leonard
,
I. D.
Couzin
, and
S. A.
Levin
,
J. Nonlinear Sci.
19
,
399
(
2009
).
10.
G.
Orosz
,
J.
Moehlis
, and
R. M.
Murray
,
Philos. Trans. R. Soc. A
368
,
439
(
2010
).
11.
W.
Wang
and
J. -J. E.
Slotine
,
IEEE Trans. Autom. Control
51
(
7
),
1156
(
2006
).
12.
L. M.
Pecora
and
T. L.
Caroll
,
Phys. Rev. Lett.
64
,
821
(
1990
).
13.
C. W.
Wu
and
L. O.
Chua
,
IEEE Trans. Circuits Syst. I: Fundam. Theory Appl.
42
,
430
(
1995
).
14.
T.
Nishikawa
and
A. E.
Motter
,
Physica D
224
,
77
(
2006
).
15.
J.
Sun
,
E. M.
Bollt
, and
T.
Nishikawa
,
Complex Sciences
(
Springer
,
Berlin
,
2009
), Vol.
4
, pp.
900
911
.
16.
L. M.
Pecora
and
T. L.
Caroll
,
Phys. Rev. Lett.
80
,
2109
(
1998
).
17.
R.
Grigoriev
,
M. C.
Cross
, and
H. G.
Schuster
,
Phys. Rev. Lett.
79
,
2795
(
1997
).
18.
F.
Sorrentino
,
M.
di Bernardo
,
F.
Garofalo
, and
G.
Chen
,
Phys. Rev. E
75
,
046103
(
2007
).
19.
M.
Porfiri
and
M.
di Bernardo
,
Automatica
44
,
3100
(
2008
).
20.
L. F. R.
Turci
and
E. E. N.
Macau
,
Phys. Rev. E
84
,
011120
(
2011
).
21.
M.
Porfiri
and
F.
Fiorilli
,
Chaos
19
,
013122
11
(
2009
).
22.
K. J.
Astrom
and
B.
Wittenmark
,
Adaptive Control
(
Addison-Wesley Reading
,
1994
).
23.
P.
De Lellis
,
M.
di Bernardo
, and
F.
Garofalo
,
Chaos
18
,
037110
(
2008
).
24.
J.
Zhou
,
J.
Lu
, and
J.
,
Automatica
44
,
996
(
2008
).
25.
A.-L.
Barabási
and
R.
Albert
,
Science
286
,
509
(
1999
).
26.
R. A.
Horn
and
C. R.
Johnson
,
Matrix Analysis
(
Cambridge University Press
,
1985
).
27.
W.
Lu
and
T.
Chen
,
Physica D
213
,
214
(
2006
).
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