Quaternion-valued Memristive Neural Networks Research Articles

Exponential State Estimation and Passivity of Fuzzy Quaternion-Valued Memristive Neural Networks: Norm Approach

Exponential State Estimation and Passivity of Fuzzy Quaternion-Valued Memristive Neural Networks: Norm Approach

Stabilization and synchronization control of quaternion-valued fuzzy memristive neural networks: Nonlinear scalarization approach

In this paper, we present new conditions ensuring existence, uniqueness, and stabilization of the equilibrium point (EP) for a large class of quaternion-valued memristive neural networks. The results are applicable to both complex-valued memristive neural networks and quaternion-valued system with uncertain terms. Subsequently, by employing suitable controller, the synchronization control conclusion is also considered. It is worth mentioning that, the nonlinear scalarization approach is employed to ensure the closed convex hull consisted by the quaternion is meaningful, which preserves the integrity of the quaternion system and makes the conclusion more reasonable. Finally, this paper provides two examples, so that the superiority of the main results can be illustrated.

An Event-Triggered Method for Stabilization of Stochastic Quaternion-Valued Memristive Neural Networks

An Event-Triggered Method for Stabilization of Stochastic Quaternion-Valued Memristive Neural Networks

Exponential control design on fixed-time synchronization of fully quaternion-valued memristive delayed neural networks without decomposition

This article mainly explores fixed-time (FXT) synchronization of fully quaternion-valued memristive neural networks (QVMNNs) with generalized delays. Firstly, based on the set-valued mapping theory and the nonsmooth approach, the discontinuity of quaternion-valued memristive connection weights is successfully solved. Next, by introducing the signum function, absolute-like norm and quadratic norm in the quaternion field, a direct non-decomposing method is put forward. Under this framework, several exponential-type controllers are designed, which have only one exponential term and no longer contain the traditional linear part and the power-law terms. Compared with designing four real-value controllers, the control schemes proposed in this article are simpler in form. Besides, several criteria of FXT synchronization and the upper bound of the setting time are deduced based on Lyapunov method and Taylor expansion. Lastly, the achieved synchronization results are confirmed via numerical examples.

Quasi-synchronization of discrete-time fractional-order quaternion-valued memristive neural networks with time delays and uncertain parameters

In this paper, quasi-synchronization of discrete-time fractional-order quaternion-valued memristive neural networks (DTFQMNNs) with time delays and uncertain parameters is investigated. Firstly, some related preliminaries are introduced and two new inequalities are obtained based on nabla fractional difference, quaternion theory and nabla h-Laplace transform. Then, a quaternion-valued controller with time delay is designed to realize quasi-synchronization goal, and some sufficient criteria are derived to guarantee quasi-synchronization of DTFQMNNs by using our created inequalities and some analysis techniques. Finally, a numerical example is provided to verify the correctness of our theoretical results.

Mittag-Leffler stability of fractional-order quaternion-valued memristive neural networks with generalized piecewise constant argument

This paper studies the global Mittag-Leffler (M-L) stability problem for fractional-order quaternion-valued memristive neural networks (FQVMNNs) with generalized piecewise constant argument (GPCA). First, a novel lemma is established, which is used to investigate the dynamic behaviors of quaternion-valued memristive neural networks (QVMNNs). Second, by using the theories of differential inclusion, set-valued mapping, and Banach fixed point, several sufficient criteria are derived to ensure the existence and uniqueness (EU) of the solution and equilibrium point for the associated systems. Then, by constructing Lyapunov functions and employing some inequality techniques, a set of criteria are proposed to ensure the global M-L stability of the considered systems. The obtained results in this paper not only extends previous works, but also provides new algebraic criteria with a larger feasible range. Finally, two numerical examples are introduced to illustrate the effectiveness of the obtained results.

Event-Triggered Finite-Time Synchronization Control for Quaternion-Valued Memristive Neural Networks by an Non-Decomposition Method

Applying the event-triggered control, this paper discusses the finite-time synchronization issue of quaternion-valued memristive neural networks (QVMNNs) with time-varying delays. By employing the improved one norm and sign function of quaternion, the QVMNNs can be analyzed as an entirety without any decomposition. To relieve the communication pressure, a proper event-triggered controller is designed, then the event-triggered conditions and some criteria are also established to guarantee finite-time synchronization. Moreover, the synchronization time is estimated by direct analysis, and the positive lower bound of the inter-event time is obtained to get rid of the Zeno behavior. In addition, according to the acquired event-triggered scheme, a self-triggered scheme is further provided to refrain from continuous detection. Ultimately, the validity of the obtained theoretical results is demonstrated by a numerical simulation.

Synchronization in fixed/preassigned-time of delayed fully quaternion-valued memristive neural networks via non-separation method

This paper mainly centers on investigating issues of synchronization of delayed memristive quaternion-valued neural networks (MQVNNs), which are first studied with an unconventional non-separation approach for the fully quaternion-valued (QV) parameters (i.e. state vectors, weights, inputs and outputs). First, QV sign function and norms are introduced and new properties of quaternions are established, which are the basis of the non-separation approach. Next, more relaxed conditions with a new pure lemma are explored to guarantee fixed-time (FXT) or preassigned-time (PST) synchronization and the settling times (STs) are measured. Specially, the ST of PST synchronization is pre-specified and irrelevant to any parameter of the systems or controllers, which is more independent. Subsequently, controller strategies are given to realize FXT and PST synchronization of the discussed systems. Lastly, the effectiveness and superiority of the achieved theoretical results are illustrated by numerical examples.

Synchronization in Fixed/Preassigned-Time of Delayed Fully Quaternion-Valued Memristive Neural Networks Via Non-Separation Method

Synchronization in Fixed/Preassigned-Time of Delayed Fully Quaternion-Valued Memristive Neural Networks Via Non-Separation Method

Quasi-stability and quasi-synchronization control of quaternion-valued fractional-order discrete-time memristive neural networks

A discrete-time fractional-order quaternion-valued memristive system is considered in this note. By utilizing contraction mapping theory, a sufficient condition for the existence and uniqueness of the equilibrium point for the considered system is derived. Via the comparison principle of linear fractional difference system, the quasi-stability condition of the given system is obtained, subsequently, the quasi-synchronization conclusion is derived through Lyapunov method and a proper controller, which can well handle the quasi-synchronization problem in the process of implementing the controller. Applying the lexicographical order method to the quaternion-valued memristive neural networks, the closed convex hull consisted by the connection weights is meaningful. One example is given to substantiate the obtained conclusions.

Finite/Fixed-Time Anti-Synchronization of Inconsistent Markovian Quaternion-Valued Memristive Neural Networks With Reaction-Diffusion Terms

In this paper, a novel class of quaternion-valued memristive neural networks (QVMNNs) that considers both the spatial factor and Markov jump phenomenon is proposed, the finite/fixed-time anti-synchronization (F/FTAS) of which is investigated. It is worth mentioning that the considered master and slave systems are assumed to jump along two inconsistent Markov chains, which is a first attempt at the issue of the anti-synchronization of Markovian systems and may be more realistic than most existing Markovian systems’ models. Then, a suitable feedback controller is designed, such that the error system can be finite/fixed-time stable. Moreover, by integrating algebraic inequality technologies and Lyapunov theory, a new F/FTAS theorem can be obtained for the proposed systems. Finally, this paper provides two examples, so that the rationality, superiority, and practical value of the main results can be illustrated.

Lagrange exponential stability of quaternion‐valued memristive neural networks with time delays

This paper investigates the Lagrange global exponential stability of the quaternion‐valued memristive neural networks (QVMNNs). Two kinds of activation functions based on different assumptions are considered. Then, based on the Lyapunov function approach, decomposition method, and some inequality skills, two novel sufficient conditions for lagrange stability of QVMNNs are provided corresponding to different types of activation functions. Lastly, simulation examples are provided to demonstrate the correctness of our theoretical results.

Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

This paper studies the global Mittag–Leffler stability and stabilization analysis of fractional-order quaternion-valued memristive neural networks (FOQVMNNs). The state feedback stabilizing control law is designed in order to stabilize the considered problem. Based on the non-commutativity of quaternion multiplication, the original fractional-order quaternion-valued systems is divided into four fractional-order real-valued systems. By using the method of Lyapunov fractional-order derivative, fractional-order differential inclusions, set-valued maps, several global Mittag–Leffler stability and stabilization conditions of considered FOQVMNNs are established. Two numerical examples are provided to illustrate the usefulness of our analytical results.

Global exponential synchronization of quaternion-valued memristive neural networks with time delays

This paper extends the memristive neural networks (MNNs) to quaternion field, a new class of neural networks named quaternion-valued memristive neural networks (QVMNNs) is then established, and the problem of drive-response global synchronization of this type of networks is investigated in this paper. Two cases are taken into consideration: one is with the conventional differential inclusion assumption, the other without. Criteria for the global synchronization of these two cases are achieved respectively by appropriately choosing the Lyapunov functional and applying some inequality techniques. Finally, corresponding simulation examples are presented to demonstrate the correctness of the proposed results derived in this paper.

Finite-Time Mittag-Leffler Stability of Fractional-Order Quaternion-Valued Memristive Neural Networks with Impulses

The finite-time Mittag-Leffler stability for fractional-order quaternion-valued memristive neural networks (FQMNNs) with impulsive effect is studied here. A new mathematical expression of the quaternion-value memductance (memristance) is proposed according to the feature of the quaternion-valued memristive and a new class of FQMNNs is designed. In quaternion field, by using the framework of Filippov solutions as well as differential inclusion theoretical analysis, suitable Lyapunov-functional and some fractional inequality techniques, the existence of unique equilibrium point and Mittag-Leffler stability in finite time analysis for considered impulsive FQMNNs have been established with the order $$0<\beta <1$$. Then, for the fractional order $$\beta $$ satisfying $$1<\beta <2$$ and by ignoring the impulsive effects, a new sufficient criterion are given to ensure the finite time stability of considered new FQMNNs system by the employment of Laplace transform, Mittag-Leffler function and generalized Gronwall inequality. Furthermore, the asymptotic stability of such system with order $$1<\beta <2$$ have been investigated. Ultimately, the accuracy and validity of obtained finite time stability criteria are supported by two numerical examples.

Exponential Stabilization Control of Delayed Quaternion-Valued Memristive Neural Networks: Vector Ordering Approach

The stabilization control of the quaternion-valued memristive system is investigated in this paper. By starting from the basic quaternion-valued algorithms, the memristive system described by quaternion-valued connection weights is derived. Subsequently, a comprehensive set of results to ensure the existence of the equilibrium point and its stability analysis have been developed. Particularly, vector ordering approach is proposed in this paper, which can be employed to determine the “magnitude” of two different quaternion-valued, and thus the closed convex hull derived by two different quaternion-valued connections can be obtained correspondingly. In the end, the proposed method is substantiated with two numerical examples.

Dissipativity and exponential state estimation for quaternion-valued memristive neural networks

In this paper, the global dissipativity and exponential state estimation for quaternion-valued memristive neural networks are investigated. By starting from basic quaternion properties, several algebraic conditions ensuring the global dissipativity and state estimation problems are derived. It is noteworthy that, based on the vector ordering approach, one can compare the “magnitude” of two different quaternion-valued, and thus the closed convex hull derived by two different quaternion-valued connections can be derived. Simulation results are given to show the validate of the mathematical model and the derived conclusions of the memristive system.

Synchronization control of quaternion-valued memristive neural networks with and without event-triggered scheme.

In this paper, the real-valued memristive neural networks (MNNs) are extended to quaternion field, a new class of neural networks named quaternion-valued memristive neural networks (QVMNNs) is then established. The problem of master-slave synchronization of this type of networks is investigated in this paper. Two types of controllers are designed: the traditional feedback controller and the event-triggered controller. Corresponding synchronization criteria are then derived based on Lyapunov method. Moreover, it is demonstrated that Zeno behavior can be avoided in case of the event-triggered strategy proposed in this work. Finally, corresponding simulation examples are proposed to demonstrate the correctness of the proposed results derived in this work.

Fixed-time synchronization of quaternion-valued memristive neural networks with time delays

In this paper, a new type of neural networks, quaternion-valued memristive neural networks (QVMNNs) is formulated. On the basis of the differential inclusion principle and the Lyapunov functional method, fixed-time synchronization problem is considered in the form of drive–response system for this type of neural networks. A novel fixed-time controller is designed to achieve the control goal. With the fixed-time stability theory and some inequality techniques, criterion of fixed-time synchronization for QVMNNs is given. Finally, corresponding simulation results are presented to show the effectiveness of the method derived in this paper.