Finite/Fixed-Time Bipartite Synchronization of Coupled Delayed Neural Networks Under a Unified Discontinuous Controller

This paper considers the finite-time and fixed-time bipartite synchronization (FFTBS) of coupled delayed neural networks (CDNNs) under signed graphs. For the structurally balanced or unbalanced network topology, both the goals of FFTBS of CDNNs are achieved simultaneously by a unified discontinuous controller. Some sufficient criterion are obtained to ensure the FFTBS under the new designed protocols, and the corresponding settling times are estimated as well. Finally, two simulations are established to verify the validity and effectiveness of the designs.

[1]  Jinde Cao,et al.  Finite-time synchronization of coupled neural networks via discontinuous controllers , 2011, Cognitive Neurodynamics.

[2]  Zhigang Zeng,et al.  Multistability of Neural Networks With Time-Varying Delays and Concave-Convex Characteristics , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[3]  Jinde Cao,et al.  Bipartite synchronization in coupled delayed neural networks under pinning control , 2018, Neural Networks.

[4]  Ji Li,et al.  Global finite-time stabilization by output feedback for planar systems without observable linearization , 2005, IEEE Transactions on Automatic Control.

[5]  Jinde Cao,et al.  Finite-/fixed-time robust stabilization of switched discontinuous systems with disturbances , 2017 .

[6]  Fuad E. Alsaadi,et al.  Fixed-Time Synchronization of Coupled Discontinuous Neural Networks with Nonidentical Perturbations , 2017, Neural Processing Letters.

[7]  Shihua Li,et al.  Finite-Time Attitude Tracking Control of Spacecraft With Application to Attitude Synchronization , 2011, IEEE Transactions on Automatic Control.

[8]  Andrey Polyakov,et al.  Finite-time and fixed-time stabilization: Implicit Lyapunov function approach , 2015, Autom..

[9]  Jinde Cao,et al.  Finite-time and fixed-time bipartite consensus of multi-agent systems under a unified discontinuous control protocol , 2017, J. Frankl. Inst..

[10]  Fuad E. Alsaadi,et al.  Bipartite consensus for multi-agent systems with antagonistic interactions and communication delays , 2018 .

[11]  Daniel W. C. Ho,et al.  Pinning Stabilization of Linearly Coupled Stochastic Neural Networks via Minimum Number of Controllers , 2009, IEEE Transactions on Neural Networks.

[12]  Deyuan Meng,et al.  Signed-average consensus for networks of agents: a nonlinear fixed-time convergence protocol , 2016 .

[13]  Tingwen Huang,et al.  Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks , 2017, Neural Networks.

[14]  Guanghui Wen,et al.  Finite-Time Bipartite Consensus for Multi-Agent Systems on Directed Signed Networks , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[15]  Wojciech Szatzschneider,et al.  An Inequality , 1991, SIAM Rev..

[16]  Haijun Jiang,et al.  Finite-time and fixed-time synchronization of discontinuous complex networks: A unified control framework design , 2018, J. Frankl. Inst..

[17]  Zhigang Zeng,et al.  Multistability of Recurrent Neural Networks With Time-varying Delays and the Piecewise Linear Activation Function , 2010, IEEE Transactions on Neural Networks.

[18]  Shihua Li,et al.  Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics , 2011, Autom..

[19]  Hongxing Yao,et al.  Adaptive synchronization of bipartite dynamical networks with distributed delays and nonlinear derivative coupling , 2011 .

[20]  M. Forti,et al.  Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations , 2006 .

[21]  Xinsong Yang,et al.  Finite-time synchronization of coupled discontinuous neural networks with mixed delays and nonidentical perturbations , 2015, J. Frankl. Inst..

[22]  Xin-Ping Guan,et al.  Finite/Fixed-Time Stabilization for Nonlinear Interconnected Systems With Dead-Zone Input , 2017, IEEE Transactions on Automatic Control.

[23]  Junping Du,et al.  Nonlinear finite-time bipartite consensus protocol for multi-agent systems associated with signed graphs , 2015, Int. J. Control.

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

[25]  Jinde Cao,et al.  Robust fixed-time synchronization for uncertain complex-valued neural networks with discontinuous activation functions , 2017, Neural Networks.

[26]  Jinde Cao,et al.  Fixed-time synchronization of delayed memristor-based recurrent neural networks , 2017, Science China Information Sciences.

[27]  Jinde Cao,et al.  Fixed-time synchronization of quaternion-valued memristive neural networks with time delays , 2019, Neural Networks.

[28]  Xiaodong Liu,et al.  Requirements model driven adaption and evolution of Internetware , 2014, Science China Information Sciences.

[29]  Jinde Cao,et al.  Finite-Time and Fixed-Time Stabilization Control of Delayed Memristive Neural Networks: Robust Analysis Technique , 2017, Neural Processing Letters.

[30]  Jinde Cao,et al.  Synchronization of coupled neural networks with random coupling strengths and mixed probabilistic time‐varying delays , 2013 .

[31]  Claudio Altafini,et al.  Consensus Problems on Networks With Antagonistic Interactions , 2013, IEEE Transactions on Automatic Control.

[32]  Tianping Chen,et al.  Synchronization of coupled connected neural networks with delays , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[33]  Zhigang Zeng,et al.  Passivity analysis of memristor-based recurrent neural networks with time-varying delays , 2013, J. Frankl. Inst..

[34]  Jinde Cao,et al.  Synchronization control of switched linearly coupled neural networks with delay , 2010, Neurocomputing.

[35]  Jinde Cao,et al.  Nonsmooth Finite-Time Synchronization of Switched Coupled Neural Networks , 2016, IEEE Transactions on Cybernetics.

[36]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[37]  Jinde Cao,et al.  Synchronization of Randomly Coupled Neural Networks With Markovian Jumping and Time-Delay , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[38]  A. Bacciotti,et al.  Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions , 1999 .

[39]  C. Altafini,et al.  Computing global structural balance in large-scale signed social networks , 2011, Proceedings of the National Academy of Sciences.

[40]  Andrey Polyakov,et al.  Robust stabilization of MIMO systems in finite/fixed time , 2016 .

[41]  Daniel W. C. Ho,et al.  Finite/Fixed-Time Pinning Synchronization of Complex Networks With Stochastic Disturbances , 2019, IEEE Transactions on Cybernetics.

[42]  JIANQUAN LU,et al.  Synchronization in an Array of Nonlinearly Coupled Chaotic Neural Networks with Delay Coupling , 2008, Int. J. Bifurc. Chaos.

[43]  Andrey Polyakov,et al.  Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems , 2012, IEEE Transactions on Automatic Control.

[44]  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.

[45]  Qiang Wang,et al.  Cluster synchronization of a class of multi-agent systems with a bipartite graph topology , 2012, Science China Information Sciences.