Fixed-time synchronization criteria for complex networks via quantized pinning control.

In this paper, fixed-time (FDT) synchronization of complex networks (CNs) is considered via quantized pinning controllers (QPCs). New control schemes with logarithmic quantization are designed, which not only can reduce control cost but also can save channel resources. The QPC with sign function can be used more generally than the QPC without sign function, but the QPC without sign function can be utilized to overcome the chattering phenomenon in some existing results. Based on designed Lyapunov function and different control schemes, several FDT synchronization criteria expressed by linear matrix inequalities (LMIs) are presented. Moreover, a numerical example is presented to illustrate the theoretical results.

[1]  Dong Yue,et al.  Quantized output feedback control for networked control systems , 2008, Inf. Sci..

[2]  Leon O. Chua,et al.  The double scroll , 1985 .

[3]  F. M. Moukam Kakmeni,et al.  Chaos control and duration time of a class of uncertain chaotic systems , 2003 .

[4]  Huaguang Zhang,et al.  A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks , 2014, IEEE Transactions on Neural Networks and Learning Systems.

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

[6]  Jinde Cao,et al.  On Pinning Controllability of Boolean Control Networks , 2016, IEEE Transactions on Automatic Control.

[7]  Junwei Wang,et al.  Synchronization of fractional-order linear complex networks. , 2015, ISA transactions.

[8]  Bing He,et al.  Distributed synchronization of networked drive-response systems: A nonlinear fixed-time protocol. , 2017, ISA transactions.

[9]  Tingwen Huang,et al.  Fixed-time synchronization of complex networks with nonidentical nodes and stochastic noise perturbations , 2018 .

[10]  R. Rakkiyappan,et al.  Synchronization of singular Markovian jumping complex networks with additive time-varying delays via pinning control , 2015, J. Frankl. Inst..

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

[12]  Yong Xu,et al.  Dynamical responses of airfoil models with harmonic excitation under uncertain disturbance , 2017 .

[13]  U. Vincent,et al.  Finite-time synchronization for a class of chaotic and hyperchaotic systems via adaptive feedback controller , 2011 .

[14]  Xinsong Yang,et al.  Finite-Time Synchronization of Coupled Networks With Markovian Topology and Impulsive Effects , 2016, IEEE Transactions on Automatic Control.

[15]  Chuandong Li,et al.  Finite-Time Synchronization of Discontinuous Neural Networks With Delays and Mismatched Parameters , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[16]  Jinde Cao,et al.  Quantized Synchronization of Chaotic Neural Networks With Scheduled Output Feedback Control , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[17]  Yong Xu,et al.  Chaos in diffusionless Lorenz System with a fractional Order and its Control , 2012, Int. J. Bifurc. Chaos.

[18]  Jürgen Kurths,et al.  The sliding mode control for an airfoil system driven by harmonic and colored Gaussian noise excitations , 2018, Applied Mathematical Modelling.

[19]  Qingling Zhang,et al.  Finite-time synchronization for second-order nonlinear multi-agent system via pinning exponent sliding mode control. , 2016, ISA transactions.

[20]  Daniel Liberzon,et al.  Quantized feedback stabilization of linear systems , 2000, IEEE Trans. Autom. Control..

[21]  Shouming Zhong,et al.  New synchronization criteria for complex delayed dynamical networks with sampled-data feedback control. , 2016, ISA transactions.

[22]  Junwei Wang,et al.  Pinning synchronization of fractional-order complex networks with Lipschitz-type nonlinear dynamics. , 2015, ISA transactions.

[23]  Lihua Xie,et al.  Robust control of a class of uncertain nonlinear systems , 1992 .

[24]  Chuandong Li,et al.  Robust Exponential Stability of Uncertain Delayed Neural Networks With Stochastic Perturbation and Impulse Effects , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[25]  Tianping Chen,et al.  A note on finite-time and fixed-time stability , 2015, Neural Networks.

[26]  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.

[27]  Fuad E. Alsaadi,et al.  Finite-Time Synchronization of Networks via Quantized Intermittent Pinning Control , 2018, IEEE Transactions on Cybernetics.

[28]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

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

[30]  Huaguang Zhang,et al.  Robust Exponential Stability of Recurrent Neural Networks With Multiple Time-Varying Delays , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[31]  Huiqing Zhang,et al.  Hopf bifurcation control for stochastic dynamical system with nonlinear random feedback method , 2011 .

[32]  Hafiz Ahmed,et al.  Robust synchronization of master-slave chaotic systems using approximate model: An experimental study. , 2018, ISA transactions.

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

[34]  Jinde Cao,et al.  Finite-time stochastic synchronization of complex networks , 2010 .

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

[36]  Jürgen Kurths,et al.  Active vibration suppression of a novel airfoil model with fractional order viscoelastic constitutive relationship , 2018, Journal of Sound and Vibration.

[37]  James Lam,et al.  Fixed-Time Synchronization of Complex Networks With Impulsive Effects via Nonchattering Control , 2017, IEEE Transactions on Automatic Control.

[38]  V. Haimo.  Finite time controllers , 1986 .

[39]  Huaguang Zhang,et al.  Robust Global Exponential Synchronization of Uncertain Chaotic Delayed Neural Networks via Dual-Stage Impulsive Control , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[40]  Zongyu Zuo,et al.  Distributed robust finite-time nonlinear consensus protocols for multi-agent systems , 2016, Int. J. Syst. Sci..

[41]  Ju H. Park,et al.  Pinning sampled-data synchronization of coupled inertial neural networks with reaction-diffusion terms and time-varying delays , 2017, Neurocomputing.

[42]  Tianping Chen,et al.  Finite-Time and Fixed-Time Cluster Synchronization With or Without Pinning Control , 2018, IEEE Transactions on Cybernetics.

[43]  Bin Hu,et al.  Quantized stabilization of wireless networked control systems with packet losses. , 2016, ISA transactions.

[44]  Mohammad Pourmahmood Aghababa,et al.  Synchronization of mechanical horizontal platform systems in finite time , 2012 .