Finite-Time and Fixed-Time Non-chattering Control for Inertial Neural Networks with Discontinuous Activations and Proportional Delay

Based on the framework of Filippov solutions, this paper considers synchronization of inertial neural networks (INNs) with discontinuous activation functions and proportional delay. By designing several non-chattering controllers, both finite-time and fixed-time synchronization are studied. The designed controllers are simple to be implemented and can overcome the effects of both nonidentical uncertainties of Filippov solutions and the proportional delay without inducing any chattering. By designing new Lyapunov functionals and utilizing 1-norm methods, several sufficient conditions are obtained to ensure that the INNs achieve drive-response synchronization in finite time and fixed time, respectively. Moreover, the settling time is estimated for the two types of synchronization. Simulations are provided to illustrate the effectiveness of theoretical analysis.

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

[2]  Jinde Cao,et al.  Stabilization of probabilistic Boolean networks via pinning control strategy , 2020, Inf. Sci..

[3]  Daniel W. C. Ho,et al.  Synchronization of Delayed Memristive Neural Networks: Robust Analysis Approach , 2016, IEEE Transactions on Cybernetics.

[4]  Kaizhong Guan,et al.  Global Asymptotic Stabilization of Cellular Neural Networks with Proportional Delay via Impulsive Control , 2019, Neural Processing Letters.

[5]  Wentao Wang,et al.  Finite-time synchronization for a class of fuzzy cellular neural networks with time-varying coefficients and proportional delays , 2017, Fuzzy Sets Syst..

[6]  Jinde Cao,et al.  Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays , 2017, Cognitive Neurodynamics.

[7]  Jigui Jian,et al.  Finite-time synchronization of inertial memristive neural networks with time-varying delays via sampled-date control , 2017, Neurocomputing.

[8]  Jinde Cao,et al.  Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches , 2011, Neural Networks.

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

[10]  Xinsong Yang,et al.  Synchronization of Time-Delayed Complex Networks With Switching Topology Via Hybrid Actuator Fault and Impulsive Effects Control , 2019, IEEE Transactions on Cybernetics.

[11]  Jinde Cao,et al.  Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays , 2014, Neural Networks.

[12]  Jianquan Lu,et al.  Synchronization of drive-response Boolean control networks with impulsive disturbances , 2020, Appl. Math. Comput..

[13]  Jinde Cao,et al.  Finite-time stabilization of switched dynamical networks with quantized couplings via quantized controller , 2017, Science China Technological Sciences.

[14]  Jinde Cao,et al.  Exponential Synchronization of Inertial Memristor-Based Neural Networks with Time Delay Using Average Impulsive Interval Approach , 2019, Neural Processing Letters.

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

[16]  Xiaotong Li,et al.  Some new results on stability and synchronization for delayed inertial neural networks based on non-reduced order method , 2017, Neural Networks.

[17]  RamanathanParameswaran,et al.  Proportional differentiated services , 1999 .

[18]  Jinde Cao,et al.  Filippov systems and quasi-synchronization control for switched networks. , 2012, Chaos.

[19]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[20]  Xinsong Yang,et al.  Can neural networks with arbitrary delays be finite-timely synchronized? , 2014, Neurocomputing.

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

[22]  Mauro Forti,et al.  Discontinuous Neural Networks for Finite-Time Solution of Time-Dependent Linear Equations , 2016, IEEE Transactions on Cybernetics.

[23]  Duccio Papini,et al.  Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain , 2005, IEEE Transactions on Neural Networks.

[24]  Haijun Jiang,et al.  Finite-time synchronization of inertial neural networks , 2017 .

[25]  Fuad E. Alsaadi,et al.  Synchronization of dynamical networks with nonlinearly coupling function under hybrid pinning impulsive controllers , 2018, J. Frankl. Inst..

[26]  Wei Xing Zheng,et al.  Dynamical Behaviors of Multiple Equilibria in Competitive Neural Networks With Discontinuous Nonmonotonic Piecewise Linear Activation Functions , 2016, IEEE Transactions on Cybernetics.

[27]  Haijun Jiang,et al.  Stability and Synchronization Analysis of Discrete-Time Delayed Neural Networks with Discontinuous Activations , 2018, Neural Processing Letters.

[28]  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.

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

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

[31]  Eryk Dutkiewicz,et al.  Cross-Layer Design for Proportional Delay Differentiation and Network Utility Maximization in Multi-Hop Wireless Networks , 2012, IEEE Transactions on Wireless Communications.

[32]  Jinde Cao,et al.  Pinning synchronization of coupled inertial delayed neural networks , 2014, Cognitive Neurodynamics.

[33]  Wen Sun,et al.  Adaptive Synchronization of Stochastic Memristor-Based Neural Networks with Mixed Delays , 2017, Neural Processing Letters.

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

[35]  G. Pólya,et al.  Inequalities (Cambridge Mathematical Library) , 1934 .

[36]  David K. Y. Yau,et al.  A proportional-delay DiffServ-enabled Web server: admission control and dynamic adaptation , 2004, IEEE Transactions on Parallel and Distributed Systems.

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

[38]  Diek W. Wheeler,et al.  Stability and chaos in an inertial two-neuron system , 1997 .

[39]  Chuandong Li,et al.  Fixed-Time Stochastic Synchronization of Complex Networks via Continuous Control , 2019, IEEE Transactions on Cybernetics.

[40]  Parameswaran Ramanathan,et al.  Proportional differentiated services: delay differentiation and packet scheduling , 1999, SIGCOMM '99.

[41]  Jinde Cao,et al.  Finite-time synchronization of complex networks with nonidentical discontinuous nodes , 2013, Nonlinear Dynamics.

[42]  Quan Yin,et al.  Synchronization Analysis of Coupled Stochastic Neural Networks with On–Off Coupling and Time-Delay , 2014, Neural Processing Letters.

[43]  Jinde Cao,et al.  Exponential Synchronization of Delayed Neural Networks With Discontinuous Activations , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[44]  Mauro Forti,et al.  Generalized neural network for nonsmooth nonlinear programming problems , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[45]  Gang Yang,et al.  Exponential Stability of Positive Recurrent Neural Networks with Multi-proportional Delays , 2018, Neural Processing Letters.

[46]  Fuad E. Alsaadi,et al.  Finite‐Time Synchronization of Complex‐Valued Delayed Neural Networks with Discontinuous Activations , 2018 .

[47]  Zhen-Hang Yang,et al.  Sharp bounds for the ratio of two zeta functions , 2020, J. Comput. Appl. Math..

[48]  M. Forti,et al.  Global convergence of neural networks with discontinuous neuron activations , 2003 .

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

[50]  Chuandong Li,et al.  Finite-Time and Fixed-Time Synchronization of Complex Networks with Discontinuous Nodes via Quantized Control , 2019, Neural Processing Letters.

[51]  Robert M. Westervelt,et al.  Stability and dynamics of simple electronic neural networks with added inertia , 1986 .

[52]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[53]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[54]  Jinde Cao,et al.  Synchronizing Neural Networks With Proportional Delays Based on a Class of $q$-Type Allowable Time Scales , 2018, IEEE Transactions on Neural Networks and Learning Systems.