Global exponential synchronization of memristor-based recurrent neural networks with time-varying delays

Finite-Time and Fixed-Time Synchronization of Delayed Memristive Neural Networks via Adaptive Aperiodically Intermittent Adjustment Strategy

This article investigates the finite-time and fixed-time synchronization for memristive neural networks (MNNs) with mixed time-varying delays under the adaptive aperiodically intermittent adjustment strategy. Different from previous works, this article first employs the aperiodically intermittent adjustment feedback control and adaptive control to drive the MNNs to achieve synchronization in finite time and fixed time. First of all, according to the theories of set-valued mappings and differential inclusions, the error MNNs is derived, and its finite-time and fixed-time stability problems are discussed by applying the Lyapunov function method and some LMI techniques. Moreover, by meticulously designing an effective aperiodically intermittent adjustment with adaptive updating law, sufficient conditions that guarantee the finite-time and fixed-time synchronization of the drive-response MNNs are obtained, and the settling time is explicitly estimated. Finally, three numerical examples are provided to illustrate the validity of the obtained theoretical results.

Event-triggered control for robust exponential synchronization of inertial memristive neural networks under parameter disturbance

Synchronization of memristive neural networks (MNNs) by using network control scheme has been widely and deeply studied. However, these researches are usually restricted to traditional continuous-time control methods for synchronization of the first-order MNNs. In this paper, we study the robust exponential synchronization of inertial memristive neural networks (IMNNs) with time-varying delays and parameter disturbance via event-triggered control (ETC) scheme. First, the delayed IMNNs with parameter disturbance are changed into first-order MNNs with parameter disturbance by constructing proper variable substitutions. Next, a kind of state feedback controller is designed to the response IMNN with parameter disturbance. Based on feedback controller, some ETC methods are provided to largely decrease the update times of controller. Then, some sufficient conditions are provided to realize robust exponential synchronization of delayed IMNNs with parameter disturbance via ETC scheme. Moreover, the Zeno behavior will not happen in all ETC conditions shown in this paper. Finally, numerical simulations are given to verify the advantages of the obtained results such as anti-interference performance and good reliability.

Multiple Mismatched Synchronization for Coupled Memristive Neural Networks With Topology-Based Probability Impulsive Mechanism on Time Scales

This article is concerned with the exponential synchronization of coupled memristive neural networks (CMNNs) with multiple mismatched parameters and topology-based probability impulsive mechanism (TPIM) on time scales. To begin with, a novel model is designed by taking into account three types of mismatched parameters, including: 1) mismatched dimensions; 2) mismatched connection weights; and 3) mismatched time-varying delays. Then, the method of auxiliary-state variables is adopted to deal with the novel model, which implies that the presented novel model can not only use any isolated system (regard as a node) in the coupled system to synchronize the states of CMNNs but also can use an external node, that is, not affiliated to the coupled system to synchronize the states of CMNNs. Moreover, the TPIM is first proposed to efficiently schedule information transmission over the network, possibly subject to a series of nonideal factors. The novel control protocol is more robust against these nonideal factors than the traditional impulsive control mechanism. By means of the Lyapunov-Krasovskii functional, robust analysis approach, and some inequality processing techniques, exponential synchronization conditions unifying the continuous-time and discrete-time systems are derived on the framework of time scales. Finally, a numerical example is provided to illustrate the effectiveness of the main results.

Adaptive Control of Advanced G-L Fuzzy Systems with Several Uncertain Terms in Membership-Matrices

In this paper, a set of novel adaptive control strategies based on an advanced G-L (proposed by Ge-Li-Tam, called GLT) fuzzy system is proposed. Three main design points can be summarized as follows: (1) the unknown parameters in a nonlinear dynamic system are regarded as extra nonlinear terms and are further packaged into so-called nonlinear terms groups for each equation through the modeling process, which reduces the complexity of the GLT fuzzy system; (2) the error dynamics are further rearranged into two parts, adjustable membership function and uncertain membership function, to aid the design of the controllers; (3) a set of adaptive controllers change with the estimated parameters and the update laws of parameters are provided following the current form of error dynamics. Two identical nonlinear dynamic systems based on a Quantum-CNN system (Q-CNN system) with two added terms are employed for simulations to demonstrate the feasibility as well as the effectiveness of the proposed fuzzy adaptive control scheme, where the tracking error can be eliminated efficiently.

Pinning multisynchronization of delayed fractional-order memristor-based neural networks with nonlinear coupling and almost-periodic perturbations

This paper concerns the multisynchronization issue for delayed fractional-order memristor-based neural networks with nonlinear coupling and almost-periodic perturbations. First, the coexistence of multiple equilibrium states for isolated subnetwork is analyzed. By means of state-space decomposition, fractional-order Halanay inequality and Caputo derivative properties, the novel algebraic sufficient conditions are derived to ensure that the addressed networks with arbitrary activation functions have multiple locally stable almost periodic orbits or equilibrium points. Then, based on the obtained multistability results, a pinning control strategy is designed to realize the multisynchronization of the N coupled networks. By the aid of graph theory, depth first search method and pinning control law, some sufficient conditions are formulated such that the considered neural networks can possess multiple synchronization manifolds. Finally, the multistability and multisynchronization performance of the considered neural networks with different activation functions are illustrated by numerical examples.

Multistability of Almost Periodic Solution for Memristive Cohen-Grossberg Neural Networks With Mixed Delays

This paper presents the multistability analysis of almost periodic state solutions for memristive Cohen-Grossberg neural networks (MCGNNs) with both distributed delay and discrete delay. The activation function of the considered MCGNNs is generalized to be nonmonotonic and nonpiecewise linear. It is shown that the MCGNNs with n -neuron have (K+1)ⁿ locally exponentially stable almost periodic solutions, where nature number K depends on the geometrical structure of the considered activation function. Compared with the previous related works, the number of almost periodic state solutions of the MCGNNs is extensively increased. The obtained conclusions in this paper are also capable of studying the multistability of equilibrium points or periodic solutions of the MCGNNs. Moreover, the enlarged attraction basins of attractors are estimated based on original partition. Some comparisons and convincing numerical examples are provided to substantiate the superiority and efficiency of obtained results.

Finite-time synchronization of memristor neural networks via interval matrix method

In this paper, the finite-time synchronization problems of two types of driven-response memristor neural networks (MNNs) without time-delay and with time-varying delays are investigated via interval matrix method, respectively. Based on interval matrix transformation, the driven-response MNNs are transformed into a kind of system with interval parameters, which is different from the previous research approaches. Several sufficient conditions in terms of linear matrix inequalities (LMIs) are driven to guarantee finite-time synchronization for MNNs. Correspondingly, two types of nonlinear feedback controllers are designed. Meanwhile, the upper-bounded of the settling time functions are estimated. Finally, two numerical examples with simulations are given to illustrate the correctness of the theoretical results and the effectiveness of the proposed controllers.

Closed-loop control of nonlinear neural networks: The estimate of control time and energy cost

This paper concentrates on an estimate of the upper bounds for control time and energy cost of a class of nonlinear neural networks (NNs). By constructing the appropriate closed-loop controller u^S and utilizing the inequality technique, sufficient conditions are proposed to guarantee achieving control target in finite time of the considered systems. Then, the estimate of the upper bounds for the control energy cost of the designed controller u^S is proposed. Our results provide a new controller which can ensure the realization of finite time control and energy consumption control for a class of nonlinear NNs. Meanwhile, the obtained results contribute to qualitative analysis of some nonlinear systems. Finally, numerical examples are presented to demonstrate the effectiveness of our theoretical results.

Quasi-Synchronization of Delayed Chaotic Memristive Neural Networks

We study the problem of master-slave synchronization of two delayed memristive neural networks (MNNs). Different from most previous papers, memristors are regarded as uncertain continuous time-varying parameters, and MNNs are modeled by neural networks (NNs) with continuous time-varying parameters and polytopic uncertainty. Thus, synchronization of two delayed MNNs is converted into synchronization of delayed NNs with uncertain parameter mismatches. Quasi-synchronization criteria are derived by Lyapunov function and inequality technique. It is shown that, given a predetermined error bound, quasi-synchronization of two delayed chaotic MNNs can be achieved provided that the pinning strength is larger than a threshold. In the end, a numerical example is provided to illustrate the effectiveness of the derived results.

Finite-Time Stabilization of Delayed Memristive Neural Networks: Discontinuous State-Feedback and Adaptive Control Approach

In this paper, a general class of delayed memristive neural networks (DMNNs) system described by functional differential equation with discontinuous right-hand side is considered. Under the extended Filippov-framework, we investigate the finite-time stabilization problem for DMNNs by using the famous finite-time stability theorem and the generalized Lyapunov functional method. To do so, we design two classes of novel controllers including discontinuous state-feedback controller and discontinuous adaptive controller. Without assuming the boundedness and monotonicity of the activation functions, several sufficient conditions are given to stabilize the states of this class of DMNNs in finite time. Moreover, the upper bounds of the settling time for stabilization are estimated. Finally, numerical examples are provided to demonstrate the effectiveness of the developed method and the theoretical results.

Scale-Limited Lagrange Stability and Finite-Time Synchronization for Memristive Recurrent Neural Networks on Time Scales

The existed results of Lagrange stability and finite-time synchronization for memristive recurrent neural networks (MRNNs) are scale-free on time evolvement, and some restrictions appear naturally. In this paper, two novel scale-limited comparison principles are established by means of inequality techniques and induction principle on time scales. Then the results concerning Lagrange stability and global finite-time synchronization of MRNNs on time scales are obtained. Scaled-limited Lagrange stability criteria are derived, in detail, via nonsmooth analysis and theory of time scales. Moreover, novel criteria for achieving the global finite-time synchronization are acquired. In addition, the derived method can also be used to study global finite-time stabilization. The proposed results extend or improve the existed ones in the literatures. Two numerical examples are chosen to show the effectiveness of the obtained results.

Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays

This paper investigates the finite-time synchronization and fixed-time synchronization problems of inertial memristive neural networks with time-varying delays. By utilizing the Filippov discontinuous theory and Lyapunov stability theory, several sufficient conditions are derived to ensure finite-time synchronization of inertial memristive neural networks. Then, for the purpose of making the setting time independent of initial condition, we consider the fixed-time synchronization. A novel criterion guaranteeing the fixed-time synchronization of inertial memristive neural networks is derived. Finally, three examples are provided to demonstrate the effectiveness of our main results.

Synchronization stability of memristor-based complex-valued neural networks with time delays

This paper focuses on the dynamical property of a class of memristor-based complex-valued neural networks (MCVNNs) with time delays. By constructing the appropriate Lyapunov functional and utilizing the inequality technique, sufficient conditions are proposed to guarantee exponential synchronization of the coupled systems based on drive-response concept. The proposed results are very easy to verify, and they also extend some previous related works on memristor-based real-valued neural networks. Meanwhile, the obtained sufficient conditions of this paper may be conducive to qualitative analysis of some complex-valued nonlinear delayed systems. A numerical example is given to demonstrate the effectiveness of our theoretical results.

Exponential Stability of Periodic Solution for Impulsive Memristor-Based Cohen–Grossberg Neural Networks with Mixed Delays

Memristor, as the future of artificial intelligence, has been widely used in pattern recognition or signal processing from sensor arrays. Memristor-based recurrent neural network (MRNN) is an ideal model to mimic the functionalities of the human brain due to the physical properties of memristor. In this paper, the periodicity for memristor-based Cohen–Grossberg neural networks (MCGNNs) is studied. The neural network (NN) considered in this paper is based on the memristor and involves time-varying delays, distributed delays and impulsive effects. The boundedness and monotonicity of the activation function are not assumed. By some inequality technique and contraction mapping principle, we prove the existence, uniqueness and exponential stability of periodic solution for MCGNNs. Finally, some numeral examples and comparisons are provided to illustrate the validation of our results.