Adaptive Fixed-Time Synchronization of Delayed Memristor-Based Neural Networks with Discontinuous Activations

Fixed-time synchronization(FTS)of delayed memristor-based neural networks(MNNs)with discontinuous activations is studied in this paper.Both continuous and discontinuous activations are considered forMNNs.And the mixed delays which are closer to reality are taken into the system.Besides,two kinds of control schemes are proposed,including feedback and adaptive control strategies.Based on some lemmas,mathematical inequalities and the designed controllers,a few synchronization criteria are acquired.Moreover,the upper bound of settling time(ST)which is independent of the initial values is given.Finally,the feasibility of our theory is attested by simulation examples.

FIXED/PREASSIGNED-TIME SYNCHRONIZATION OF QUATERNION-VALUED NEURAL NETWORKS INVOLVING DELAYS AND DISCONTINUOUS ACTIVATIONS: A DIRECT APPROACH

The fixed-time synchronization and preassigned-time synchronization are investigated for a class of quaternion-valued neural networks with time-varying delays and discontinuous activation functions. Unlike previous efforts that employed separation analysis and the real-valued control design, based on the quaternion-valued signum function and several related properties, a direct analytical method is proposed here and the quaternion-valued controllers are designed in order to discuss the fixed-time synchronization for the relevant quaternion-valued neural networks. In addition, the preassigned-time synchronization is investigated based on a quaternion-valued control design, where the synchronization time is preassigned and the control gains are finite. Compared with existing results, the direct method without separation developed in this article is beneficial in terms of simplifying theoretical analysis, and the proposed quaternion-valued control schemes are simpler and more effective than the traditional design, which adds four real-valued controllers. Finally, two numerical examples are given in order to support the theoretical results.

Multistability of delayed complex-valued recurrent neural networks with discontinuous real-imaginarytype activation functions

In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.

Robust fuzzy control of Takagi-Sugeno fuzzy neural networks with discontinuous activation functions and time delays

The problem of global robust asymptotical stability for a class of Takagi-Sugeno fuzzy neural networks（TSFNN） with discontinuous activation functions and time delays is investigated by using Lyapunov stability theory.Based on linear matrix inequalities（LMIs）,we originally propose robust fuzzy control to guarantee the global robust asymptotical stability of TSFNNs.Compared with the existing literature,this paper removes the assumptions on the neuron activations such as Lipschitz conditions,bounded,monotonic increasing property or the right-limit value is bigger than the left one at the discontinuous point.Thus,the results are more general and wider.Finally,two numerical examples are given to show the effectiveness of the proposed stability results.

General Decay Synchronization of Competitive Fuzzy Neural Networks Involving Time Delays and Right-Hand Discontinuous Activation

This paper discusses the general decay synchronization problem for a class of fuzzy competitive neural networks with time-varying delays and discontinuous activation functions. Firstly, based on the concept of Filippov solutions for right-hand discontinuous systems, some sufficient conditions for general decay synchronization of the considered system are obtained via designing a nonlinear feedback controller and applying discontinuous differential equation theory, Lyapunov functional methods and some inequality techniques. Finally, one numerical example is given to verify the effectiveness of the proposed theoretical results. The general decay synchronization considered in this article can better estimate the convergence rate of the system, and the exponential synchronization and polynomial synchronization can be seen as its special cases.

Prescribed finite-time stabilization of fuzzy neural networks with time-varying controller

This paper investigates the exponential and prescribed finite-time stabilization with time-varying controller.First,the constraints of boundedness and differentiability on time delays are simultaneously relaxed,the Lipschitz condition for activation function is also relaxed.Second,different from the traditional Lyapunov function,two different time-varying Lyapunov functions are respectively constructed to achieve the exponential and prescribed finite-time stabilization.Significantly,the exponential convergence rate and the settling time are constants that can be given in advance and are not affected by system parameters and initial states.In addition,the time-varying controllers have good tolerance for disturbance caused by discontinuous functions and the disturbance is perfectly resolved and does not affect the control performance.Especially,the form of controllers is relatively simple and there is not necessary to design the fractional-order controllers for prescribed finite-time stabilization.Furthermore,the exponential and prescribed finite-time stabilization for FNNs without delay are respectively established via continuous time-varying state feedback control.Finally,examples show the effectiveness of the proposed control methods.

Dynamical behaviors of recurrently connected neural networks and linearly coupled networks with discontinuous right-hand sides

The aim of this paper is to provide a sys- tematic review on the framework to analyze dynamics in recurrently connected neural networks with discontinu- ous right-hand sides with a focus on the authors＇ works in the past three years. The concept of the Filippov so- lution is employed to define the solution of the neural network systems by transforming them to differential in- clusions. The theory of viability provides a tool to study the existence and uniqueness of the solution and the Lya- punov function （functional） approach is used to investi- gate the global stability and synchronization. More pre- cisely, we prove that the diagonal-dominant conditions guarantee the existence, uniqueness, and stability of a general class of integro-differential equations with （al- most） periodic self-inhibitions, interconnection weights, inputs, and delays. This model is rather general and in- cludes the well-known Hopfield neural networks, Cohen- Grossberg neural networks, and cellular neural networks as special cases. We extend the absolute stability anal- ysis of gradient-like neural network model by relaxing the analytic constraints so that they can be employed to solve optimization problem with non-smooth cost func- tions. Furthermore, we study the global synchronization problem of a class of linearly coupled neural network with discontinuous right-hand sides.

Robust stability of mixed Cohen–Grossberg neural networks with discontinuous activation functions

Purpose–The purpose of this paper is to develop a method for the existence,uniqueness and globally robust stability of the equilibrium point for Cohen–Grossberg neural networks with time-varying delays,continuous distributed delays and a kind of discontinuous activation functions.Design/methodology/approach–Basedonthe Leray–Schauderalternativetheoremand chainrule,by using a novel integral inequality dealing with monotone non-decreasing function,the authors obtain a delay-dependent sufficient condition with less conservativeness for robust stability of considered neural networks.Findings–Itturns out thattheauthors’delay-dependent sufficientcondition canbeformed intermsof linear matrix inequalities conditions.Two examples show the effectiveness of the obtained results.Originality/value–The novelty of the proposed approach lies in dealing with a new kind of discontinuous activation functions by using the Leray–Schauder alternative theorem,chain rule and a novel integral inequality on monotone non-decreasing function.

μ-stability of multiple equilibria in Cohen-Grossberg neural networks and its application to associative memory

In this paper, the μ-stability of multiple equilibrium points(EPs) in the Cohen-Grossberg neural networks(CGNNs) is addressed by designing a kind of discontinuous activation function(AF). Under some criteria, CGNNs with this AF are shown to possess at least 5^(n)EPs, of which 3^(n)EPs are locally μ-stable. Compared with the saturated AF or the sigmoidal AF, CGNNs with the designed AF can produce many more total/stable EPs. Therefore, when CGNNs with the designed discontinuous AF are applied to associative memory, they can store more prototype patterns. Moreover, the AF is expanded to a more general version to further increase the number of total/stable equilibria. The CGNNs with the expanded AF are found to produce(2k+3)^(n)EPs, of which (k+2)^(n)EPs are locally μ-stable. By adjusting two parameters in the AF, the number of sufficient conditions ensuring the μ-stability of multiple equilibria can be decreased. This finding implies that the computational complexity can be greatly reduced.Two numerical examples and an application to associative memory are illustrated to verify the correctness of the obtained results.