Finite-Time Stabilization and Adaptive Control of Memristor-Based Delayed Neural Networks

Finite-time stability problem has been a hot topic in control and system engineering. This paper deals with the finite-time stabilization issue of memristor-based delayed neural networks (MDNNs) via two control approaches. First, in order to realize the stabilization of MDNNs in finite time, a delayed state feedback controller is proposed. Then, a novel adaptive strategy is applied to the delayed controller, and finite-time stabilization of MDNNs can also be achieved by using the adaptive control law. Some easily verified algebraic criteria are derived to ensure the stabilization of MDNNs in finite time, and the estimation of the settling time functional is given. Moreover, several finite-time stability results as our special cases for both memristor-based neural networks (MNNs) without delays and neural networks are given. Finally, three examples are provided for the illustration of the theoretical results.

[1]  Zhihong Man,et al.  Finite-time stabilization of stochastic nonlinear systems in strict-feedback form , 2013, Autom..

[2]  Zhigang Zeng,et al.  Multistability of Two Kinds of Recurrent Neural Networks With Activation Functions Symmetrical About the Origin on the Phase Plane , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[3]  Wei Xing Zheng,et al.  Finite-time stabilization for a class of switched time-delay systems under asynchronous switching , 2013, Appl. Math. Comput..

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

[5]  Gang Feng,et al.  Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems , 2012, Autom..

[6]  Jinde Cao,et al.  Global exponential stability and periodicity of recurrent neural networks with time delays , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[7]  Jinde Cao,et al.  A new switching design to finite-time stabilization of nonlinear systems with applications to neural networks , 2014, Neural Networks.

[8]  Tingwen Huang,et al.  Exponential stabilization of delayed recurrent neural networks: A state estimation based approach , 2013, Neural Networks.

[9]  Huaguang Zhang,et al.  On Stabilization of Stochastic Cohen-Grossberg Neural Networks With Mode-Dependent Mixed Time-Delays and Markovian Switching , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[10]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[11]  Zhigang Zeng,et al.  Lagrange Stability of Memristive Neural Networks With Discrete and Distributed Delays , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[12]  Ligang Wu,et al.  Event-Triggered Control for Nonlinear Systems Under Unreliable Communication Links , 2017, IEEE Transactions on Fuzzy Systems.

[13]  Lijie Wang,et al.  Adaptive Fuzzy Control for Nonstrict-Feedback Systems With Input Saturation and Output Constraint , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[14]  Wei Xing Zheng,et al.  Impulsive Stabilization and Impulsive Synchronization of Discrete-Time Delayed Neural Networks , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[15]  Haijun Jiang,et al.  Finite-time synchronization of delayed neural networks with Cohen-Grossberg type based on delayed feedback control , 2014, Neurocomputing.

[16]  Leimin Wang,et al.  Finite-Time Stabilizability and Instabilizability of Delayed Memristive Neural Networks With Nonlinear Discontinuous Controller , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[17]  Lihong Huang,et al.  Finite-time stabilization control of memristor-based neural networks☆ , 2016 .

[18]  Zhidong Teng,et al.  Finite-time synchronization for memristor-based neural networks with time-varying delays , 2015, Neural Networks.

[19]  Jun Wang,et al.  Robustness Analysis of Global Exponential Stability of Recurrent Neural Networks in the Presence of Time Delays and Random Disturbances , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[20]  Lihong Huang,et al.  Finite-time stabilization control for discontinuous time-delayed networks: New switching design , 2016, Neural Networks.

[21]  Ligang Wu,et al.  Receding Horizon Stabilization and Disturbance Attenuation for Neural Networks With Time-Varying Delay , 2015, IEEE Transactions on Cybernetics.

[22]  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.

[23]  Leon O. Chua,et al.  Memristor Bridge Synapse-Based Neural Network and Its Learning , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[24]  Iasson Karafyllis,et al.  Finite-Time Global Stabilization by Means of Time-Varying Distributed Delay Feedback , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[25]  Wilfrid Perruquetti,et al.  Finite-time stability and stabilization of time-delay systems , 2008, Syst. Control. Lett..

[26]  Choon Ki Ahn $l_{2}-l_{\infty}$ Suppression of Limit Cycles in Interfered Two-Dimensional Digital Filters: A Fornasini–Marchesini Model Case , 2014, IEEE Transactions on Circuits and Systems II: Express Briefs.

[27]  Emilia Fridman,et al.  Comments on finite-time stability of time-delay systems , 2014, Autom..

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

[29]  Yongduan Song,et al.  Adaptive finite-time consensus control of a group of uncertain nonlinear mechanical systems , 2015, Autom..

[30]  Zhigang Zeng,et al.  Circuit design and exponential stabilization of memristive neural networks , 2015, Neural Networks.

[31]  Zhigang Zeng,et al.  Exponential Stabilization of Memristive Neural Networks With Time Delays , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[32]  Leon O. Chua,et al.  MEMRISTOR CELLULAR AUTOMATA AND MEMRISTOR DISCRETE-TIME CELLULAR NEURAL NETWORKS , 2009 .

[33]  Wilfrid Perruquetti,et al.  Finite time stability of differential inclusions , 2005, IMA J. Math. Control. Inf..

[34]  Massimiliano Di Ventra,et al.  Experimental demonstration of associative memory with memristive neural networks , 2009, Neural Networks.

[35]  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.

[36]  Hieu Minh Trinh,et al.  Exponential Stabilization of Neural Networks With Various Activation Functions and Mixed Time-Varying Delays , 2010, IEEE Transactions on Neural Networks.

[37]  Yuzhen Wang,et al.  Finite-Time Stability and Stabilization of a Class of Nonlinear Time-Delay Systems , 2012, SIAM J. Control. Optim..

[38]  Jun Wang,et al.  Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays , 2013, Neural Networks.

[39]  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.

[40]  Quan Yin,et al.  Global exponential periodicity and stability of a class of memristor-based recurrent neural networks with multiple delays , 2013, Inf. Sci..

[41]  Xin Wang,et al.  Delay-dependent robust stability and stabilization of uncertain memristive delay neural networks , 2014, Neurocomputing.

[42]  Abdesselem Boulkroune,et al.  Adaptive Fuzzy Backstepping Tracking Control for Strict-Feedback Systems With Input Delay , 2017, IEEE Transactions on Fuzzy Systems.

[43]  Quan Yin,et al.  Adaptive Synchronization of Memristor-Based Neural Networks with Time-Varying Delays , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[44]  Zhidong Teng,et al.  Exponential stabilization and synchronization of neural networks with time-varying delays via periodically intermittent control , 2010 .

[45]  Guodong Zhang,et al.  Global anti-synchronization of a class of chaotic memristive neural networks with time-varying delays , 2013, Neural Networks.

[46]  Bin Jiang,et al.  LMI-Based Approach for Global Asymptotic Stability Analysis of Recurrent Neural Networks with Various Delays and Structures , 2011, IEEE Transactions on Neural Networks.

[47]  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.

[48]  Guodong Zhang,et al.  Exponential Stabilization of Memristor-based Chaotic Neural Networks with Time-Varying Delays via Intermittent Control , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[49]  Lihong Huang,et al.  Finite time stability of periodic solution for Hopfield neural networks with discontinuous activations , 2013, Neurocomputing.