Adaptive finite-time synchronization of a class of pinned and adjustable complex networks

This paper is concerned with the finite-time asymptotic synchronization problem of a class of dynamical complex networks with adjustable couplings. Pinning controllers are developed to guarantee that synchronization errors of pinned nodes converge to zero within finite-time. The effects of couplings in networks are further studied, and adaptive schemes for adjusting coupled strength are provided to ensure the finite-time synchronization of unpinned nodes. Through the Lyapunov function and adaptive schemes, some results indicating that control strategies and coupling adjustment laws can guarantee the asymptotic synchronization of pinned and unpinned nodes within finite-time respectively, are obtained. Simulation results are given to verify the effectiveness of the proposed method.

[1]  Yu Tang,et al.  Terminal sliding mode control for rigid robots , 1998, Autom..

[2]  Stephen P. Boyd,et al.  Analysis and Synthesis of State-Feedback Controllers With Timing Jitter , 2009, IEEE Transactions on Automatic Control.

[3]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[4]  Junan Lu,et al.  Adaptive synchronization of an uncertain complex dynamical network , 2006, IEEE Transactions on Automatic Control.

[5]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[6]  Xinghuo Yu,et al.  Finite-time synchronization of neutral complex networks with Markovian switching based on pinning controller , 2015, Neurocomputing.

[7]  Wei Xing Zheng,et al.  Exponential Synchronization of Complex Networks of Linear Systems and Nonlinear Oscillators: A Unified Analysis , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Wenwu Yu,et al.  Distributed Consensus Filtering in Sensor Networks , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[9]  Jürgen Kurths,et al.  Complex Dynamics in Physiological Systems: From Heart to Brain , 2009 .

[10]  Yuhua Xu,et al.  Finite-time synchronization of the complex dynamical network with non-derivative and derivative coupling , 2016, Neurocomputing.

[11]  Licheng Jiao,et al.  Robust adaptive global synchronization of complex dynamical networks by adjusting time-varying coupling strength , 2008 .

[12]  Huijun Gao,et al.  On Discrete-Time Convergence for General Linear Multi-Agent Systems Under Dynamic Topology , 2014, IEEE Transactions on Automatic Control.

[13]  Guang-Hong Yang,et al.  Adaptive Synchronization of a Class of Uncertain Complex Networks Against Network Deterioration , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  Junan Lu,et al.  Pinning a Complex Delayed Dynamical Network to a Homogenous Trajectory , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[15]  Tianping Chen,et al.  Pinning Complex Networks by a Single Controller , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  Song Zheng,et al.  Adaptive projective synchronization in complex networks with time-varying coupling delay , 2009 .

[17]  Guanrong Chen,et al.  Robust adaptive synchronization of uncertain dynamical networks , 2004 .

[18]  Wenwu Yu,et al.  Synchronization on Complex Networks of Networks , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[19]  Tao Li,et al.  Finite-Time Consensus for Leader-Following Second-Order Multi-Agent Networks , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  Huijun Gao,et al.  Coordination for Linear Multiagent Systems With Dynamic Interaction Topology in the Leader-Following Framework , 2014, IEEE Transactions on Industrial Electronics.

[21]  Huijun Gao,et al.  Cluster synchronization in directed networks of partial-state coupled linear systems under pinning control , 2014, Autom..

[22]  Lin Huang,et al.  Stability analysis and decentralized control of a class of complex dynamical networks , 2008, Autom..

[23]  Yigang He,et al.  Finite-Time Synchronization of a Class of Second-Order Nonlinear Multi-Agent Systems Using Output Feedback Control , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Finite-Time Rendezvous Algorithms for Mobile Autonomous Agents , 2011, IEEE Transactions on Automatic Control.

[25]  Alessandro Giua,et al.  Finite-Time Consensus With Disturbance Rejection by Discontinuous Local Interactions in Directed Graphs , 2015, IEEE Transactions on Automatic Control.

[26]  Jinde Cao,et al.  On Pinning Synchronization of Directed and Undirected Complex Dynamical Networks , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[27]  Zheng-Guang Wu,et al.  Robust $\mathcal{H}_{\infty}$ decentralized dynamic control for synchronization of a complex dynamical network with randomly occurring uncertainties , 2012 .

[28]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[29]  Zhiyong Geng,et al.  Finite-time formation control for linear multi-agent systems: A motion planning approach , 2015, Syst. Control. Lett..

[30]  Zidong Wang,et al.  Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[31]  Ju H. Park.  Synchronization of Genesio chaotic system via backstepping approach , 2006 .

[32]  Xiaoqing Lu,et al.  Finite-Time Distributed Tracking Control for Multi-Agent Systems With a Virtual Leader , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[33]  S. M. Lee,et al.  Synchronization for chaotic Lur’e systems with sector-restricted nonlinearities via delayed feedback control , 2009 .

[34]  Xiao Fan Wang,et al.  Complex Networks: Topology, Dynamics and Synchronization , 2002, Int. J. Bifurc. Chaos.

[35]  Xiaohong Wang,et al.  Finite-time synchronization of drive-response systems via periodically intermittent adaptive control , 2014, J. Frankl. Inst..

[36]  Shihua Chen,et al.  Pinning synchronization of the complex networks with non-delayed and delayed coupling , 2009 .

[37]  Daniel W. C. Ho,et al.  Finite-Time Cluster Synchronization of T–S Fuzzy Complex Networks With Discontinuous Subsystems and Random Coupling Delays , 2015, IEEE Transactions on Fuzzy Systems.

[38]  Renquan Lu,et al.  Asynchronous Dissipative State Estimation for Stochastic Complex Networks With Quantized Jumping Coupling and Uncertain Measurements , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[39]  Xiaoyang Liu,et al.  A Switching Approach to Designing Finite-Time Synchronization Controllers of Coupled Neural Networks , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[40]  Frank L. Lewis,et al.  Finite-time distributed consensus via binary control protocols , 2011, Autom..

[41]  Long Wang,et al.  Finite-time formation control for multi-agent systems , 2009, Autom..

[42]  Junan Lu,et al.  Structure identification of uncertain general complex dynamical networks with time delay , 2009, Autom..

[43]  Xiao-Zheng Jin,et al.  Active coupling and its circuitry designs of chaotic systems against deteriorated and delayed networks , 2012 .

[44]  Engin Yaz,et al.  Sliding-Mode Adaptive Observer Approach to Chaotic Synchronization , 2000 .

[45]  Guanghui Wen,et al.  Finite-time consensus for second-order multi-agent systems with saturated control protocols , 2015 .

[46]  Wenwu Yu,et al.  On pinning synchronization of complex dynamical networks , 2009, Autom..