Finite-time adaptive synchronization of fractional-order delayed quaternion-valued fuzzy neural networks

Based on direct quaternion method, this paper explores the finite-time adaptive synchronization (FAS) of fractional-order delayed quaternion-valued fuzzy neural networks (FODQVFNNs). Firstly, a useful fractional differential inequality is created, which offers an effective way to investigate FAS. Then two novel quaternion-valued adaptive control strategies are designed. By means of our newly proposed inequality, the basic knowledge about fractional calculus, reduction to absurdity as well as several inequality techniques of quaternion and fuzzy logic, several sufficient FAS criteria are derived for FODQVFNNs. Moreover, the settling time of FAS is estimated, which is in connection with the order and initial values of considered systems as well as the controller parameters. Ultimately, the validity of obtained FAS criteria is corroborated by numerical simulations

Finite-time stabilization for fractional-order inertial neural networks with time varying delays

This paper deals with the finite-time stabilization of fractional-order inertial neural network with varying time-delays (FOINNs). Firstly, by correctly selected variable substitution, the system is transformed into a first-order fractional differential equation. Secondly, by building Lyapunov functionalities and using analytical techniques, as well as new control algorithms (which include the delay-dependent and delay-free controller), novel and effective criteria are established to attain the finite-time stabilization of the addressed system. Finally, two examples are used to illustrate the effectiveness and feasibility of the obtained results

Finite-time passivity for neutral-type neural networks with time-varying delays – via auxiliary function-based integral inequalities

In this paper, we investigated the problem of the finite-time boundedness and finitetime passivity for neural networks with time-varying delays. A triple, quadrable and five integral terms with the delay information are introduced in the new Lyapunov–Krasovskii functional (LKF). Based on the auxiliary integral inequality, Writinger integral inequality and Jensen’s inequality, several sufficient conditions are derived. Finally, numerical examples are provided to verify the effectiveness of the proposed criterion. There results are compared with the existing results.&nbsp

Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations

In this paper, finite-time synchronization of neural networks (NNs) with discontinuous activation functions (DAFs), Markovian switching, and proportional delays is studied in the framework of Filippov solution. Since proportional delay is unbounded and different from infinite-time distributed delay and classical finite-time analytical techniques are not applicable anymore, new 1-norm analytical techniques are developed. Controllers with and without the sign function are designed to overcome the effects of the uncertainties induced by Filippov solutions and further synchronize the considered NNs in a finite time. By designing new Lyapunov functionals and using M-matrix method, sufficient conditions are derived to guarantee that the considered NNs realize synchronization in a settling time without introducing any free parameters. It is shown that, though the proportional delay can be unbounded, complete synchronization can still be realized, and the settling time can be explicitly estimated. Moreover, it is discovered that controllers with sign function can reduce the control gains, while controllers without the sign function can overcome chattering phenomenon. Finally, numerical simulations are given to show the effectiveness of theoretical results

Finite-Time Boundedness of Impulsive Delayed Reaction–Diffusion Stochastic Neural Networks

Considering the impulsive delayed reaction&amp;#x2013;diffusion stochastic neural networks (IDRDSNNs) with hybrid impulses, the finite-time boundedness (FTB) and finite-time contractive boundedness (FTCB) are investigated in this article. First, a novel delay integral inequality is presented. By integrating this inequality with the comparison principle, some sufficient conditions that ensure the FTB and FTCB of IDRDSNNs are obtained. This study demonstrates that the FTB of neural networks with hybrid impulses can be maintained, even in the presence of impulsive perturbations. And for a system that is not FTB due to impulsive perturbations, achieving FTB is possible through the implementation of appropriate impulsive control and optimization of the average impulsive intervals. In addition, to validate the practicality of our results, three illustrative examples are provided. In the end, these theoretical findings are successfully applied to image encryption.</p

Finite-Time Boundedness of Impulsive Delayed Reaction–Diffusion Stochastic Neural Networks

Considering the impulsive delayed reaction&amp;#x2013;diffusion stochastic neural networks (IDRDSNNs) with hybrid impulses, the finite-time boundedness (FTB) and finite-time contractive boundedness (FTCB) are investigated in this article. First, a novel delay integral inequality is presented. By integrating this inequality with the comparison principle, some sufficient conditions that ensure the FTB and FTCB of IDRDSNNs are obtained. This study demonstrates that the FTB of neural networks with hybrid impulses can be maintained, even in the presence of impulsive perturbations. And for a system that is not FTB due to impulsive perturbations, achieving FTB is possible through the implementation of appropriate impulsive control and optimization of the average impulsive intervals. In addition, to validate the practicality of our results, three illustrative examples are provided. In the end, these theoretical findings are successfully applied to image encryption.</p

Synchronization of Complex Dynamical Networks via Event-Triggered Pinning Impulses

This article studies the synchronization problem of complex dynamical networks. The impulsive control method is considered with a novel event-triggered pinning algorithm. Sufficient conditions on the network topology are obtained to ensure network synchronization. It is shown that synchronization can be realized with a careful selection of the pinning nodes. Furthermore, an adaptive coupling strength is incorporated into the network to allow network synchronization with an arbitrary selection of the pinning nodes. An example of a network with node dynamics described by the Chen system is studied to demonstrate the theoretical results

Synchronization of Complex-Valued Dynamical Networks

Dynamical networks (DNs) have been broadly applied to describe natural and human systems consisting of a large number of interactive individuals. Common examples include Internet, food webs, social networks, neural networks, etc. One of the crucial and significant collective behaviors of DNs is known as synchronization. In reality, synchronization phenomena may occur either inside a network or between two or more networks, which are called “inner synchronization” and “outer synchronization”, respectively. On the other hand, many real systems are more suitably characterized by complex-valued dynamical systems, such as quantum systems, complex Lorenz system, and complex-valued neural networks. The main focus of this thesis is on synchronization of complex-valued dynamical networks (CVDNs). In this thesis, we firstly design a delay-dependent pinning impulsive controller to study synchronization of time-delay CVDNs. By taking advantage of the Lyapunov function in the complex field, some delay-independent synchronization criteria of CVDNs are established, which generalizes some existing synchronization results. Then, by employing the Lyapunov functional in the complex field, several delay-dependent sufficient conditions on synchronization of CVDNs with various sizes of delays are constructed. Moreover, we study synchronization of CVDNs with time-varying delays under distributed impulsive controllers. By taking advantage of time-varying Lyapunov function/ functional in the complex domain, several synchronization criteria for CVDNs with time-varying delays are derived in terms of complex-valued linear matrix inequalities (LMIs). Then, we propose a memory-based event-triggered impulsive control (ETIC) scheme with three levels of events in the complex field to investigate the synchronization problem of CVDNs with both discrete and distributed time delays, and we further consider an event-triggered pinning impulsive control (ETPIC) scheme combining the proposed ETIC and a pinning algorithm to study synchronization of time-delay CVDNs. Results show that the proposed ETIC scheme and ETPIC scheme can effectively synchronize CVDNs with the desired trajectory. Secondly, we study generalized outer synchronization of drive-response time-delayed CVDNs via hybrid control. A hybrid controller is proposed in the complex domain to construct response complex-valued networks. Some generalized outer synchronization criteria for drive-response CVDNs are established, which extend the existing generalized outer synchronization results to the complex field. Thirdly, we study the average-consensus problem of potential complex-valued multi-agent systems. A complex-variable hybrid consensus protocol is proposed, and time delays are taken into account in both the continuous-time protocol and the discrete-time protocol. Delay-dependent sufficient conditions are established to guarantee the proposed complex-variable hybrid consensus protocol can solve the average-consensus problem. Lastly, as a practical application for complex-valued networked systems, the synchronization problem of master-slave complex-valued neural networks (CVNNs) is studied via hybrid control and delayed ETPIC, respectively. We also investigate the state estimation problem of CVNNs by designing the adaptive impulsive observer in the complex field

Quantized passive filtering for switched delayed neural networks

The issue of quantized passive filtering for switched delayed neural networks with noise interference is studied in this paper. Both arbitrary and semi-Markov switching rules are taken into account. By choosing Lyapunov functionals and applying several inequality techniques, sufficient conditions are proposed to ensure the filter error system to be not only exponentially stable, but also exponentially passive from the noise interference to the output error. The gain matrix for the proposed quantized passive filter is able to be determined through the feasible solution of linear matrix inequalities, which are computationally tractable with the help of some popular convex optimization tools. Finally, two numerical examples are given to illustrate the usefulness of the quantized passive filter design methods