Adaptive node-to-node pinning synchronization control of complex networks.

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]  Romeo Ortega,et al.  Proceedings of the 40th IEEE Conference on Decision and Control, 2001 , 2001 .

[2]  Maurizio Porfiri,et al.  Criteria for global pinning-controllability of complex networks , 2008, Autom..

[3]  I. Couzin,et al.  Effective leadership and decision-making in animal groups on the move , 2005, Nature.

[4]  Karl Johan Åström,et al.  Adaptive Control , 1989, Embedded Digital Control with Microcontrollers.

[5]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[6]  Sonia Martínez,et al.  Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions , 2006, IEEE Transactions on Automatic Control.

[7]  Gábor Orosz,et al.  Controlling biological networks by time-delayed signals , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[8]  Naomi Ehrich Leonard,et al.  Dynamics of Decision Making in Animal Group Motion , 2009, J. Nonlinear Sci..

[9]  R. Rosenfeld Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[10]  F. Garofalo,et al.  Synchronization of complex networks through local adaptive coupling. , 2008, Chaos.

[11]  L. Chua,et al.  Synchronization in an array of linearly coupled dynamical systems , 1995 .

[12]  M. Porfiri,et al.  Node-to-node pinning control of complex networks. , 2009, Chaos.

[13]  Complex Sciences , 2012, Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering.

[14]  J. Rogers Chaos , 1876 .

[15]  F. Garofalo,et al.  Controllability of complex networks via pinning. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Tianping Chen,et al.  New approach to synchronization analysis of linearly coupled ordinary differential systems , 2006 .

[17]  Jean-Jacques E. Slotine,et al.  A theoretical study of different leader roles in networks , 2006, IEEE Transactions on Automatic Control.

[18]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[19]  M. Cross,et al.  Pinning control of spatiotemporal chaos , 1997, chao-dyn/9705001.

[20]  Jie Sun,et al.  Synchronization Stability of Coupled Near-Identical Oscillator Network , 2009, Complex.

[21]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[22]  E. Ott,et al.  Adaptive synchronization of dynamics on evolving complex networks. , 2008, Physical review letters.

[23]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[24]  Naomi Ehrich Leonard,et al.  Stabilization of symmetric formations to motion around convex loops , 2008, Syst. Control. Lett..

[25]  Adilson E. Motter,et al.  Maximum performance at minimum cost in network synchronization , 2006, cond-mat/0609622.

[26]  Junan Lu,et al.  Pinning adaptive synchronization of a general complex dynamical network , 2008, Autom..

[27]  Luiz Felipe R Turci,et al.  Performance of pinning-controlled synchronization. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  R. Sepulchre,et al.  Oscillator Models and Collective Motion , 2007, IEEE Control Systems.

[29]  Edward Ott,et al.  Dynamic synchronization of a time-evolving optical network of chaotic oscillators. , 2010, Chaos.

[30]  T. Carroll,et al.  Master Stability Functions for Synchronized Coupled Systems , 1998 .