Stability and Synchronization of Nonautonomous Reaction-Diffusion Neural Networks With General Time-Varying Delays

Observer-Based Boundary Stabilization of Coupled Semilinear Reaction-Diffusion Neural Networks With Spatially Varying Coefficients via Event-Triggered Controller

The aim of this article is to propose an observer-based event-triggered Robin boundary control strategy for the exponential stabilization of the coupled semilinear reaction-diffusion neural networks with spatially varying coefficients. Toward this aim, we design an observer to estimate the value of system states by using some of these system values as the available measurement. An observer-based event-triggered boundary stabilizer is then presented to exponentially stabilize the considered systems with the Zeno behavior being excluded. Throughout this article, the main used method is backstepping, which yields an explicit expression of the control formulae. Moreover, we see that the proposed event-triggered boundary control scheme can ensure the desired level of control performance with fewer control law updates. A numerical example is finally given to illustrate the effectiveness of our proposed method.

Exponential Stabilization of Semi-Markov Reaction-Diffusion Memristive NNs via Event-Based Spatially Pointwise-Piecewise Switching Control

This article considers both the semi-Markov jumping phenomenon and spatial distribution characteristics when investigating the exponential stabilization of memristive neural networks (MNNs). The introduction of the semi-Markov jumping parameters relaxes the restriction on the sojourn time of Markovian MNNs. To increase the operability while ensuring control effect, a novel event-based spatially pointwise-piecewise switching control scheme is presented under a unified spatial division criterion, in which the pointwise and piecewise control can switch according to the preset event condition for the applicability to different control requirements. Moreover, by constructing a semi-Markov Lyapunov functional and utilizing the properties of the considered cumulative distribution function, the final exponential stabilization criterion and two related corollaries are obtained. Finally, simulation results illustrate the effectiveness and superiority of the proposed control strategy.

Fixed-time periodic stabilization of discontinuous reaction-diffusion Cohen-Grossberg neural networks

This paper aims to study the fixed-time stabilization of a class of delayed discontinuous reaction-diffusion Cohen-Grossberg neural networks. Firstly, by providing some relaxed conditions containing indefinite functions and based on inequality techniques, a new fixed-time stability lemma is given, which can improve the traditional ones. Secondly, based on state-dependent switching laws, the periodic wave solution of the formulated networks is transformed into the periodic solution of ordinary differential system. By utilizing differential inclusions theory and coincidence theorem, the existence of periodic solutions is obtained. Thirdly, based on the new fixed-time stability lemma, the periodic solutions are stabilized at zero in a fixed-time, which is a new topic on reaction-diffusion networks. Moreover, the established criteria are all delay-dependent, which are less conservative than the previous delay-independent ones for ensuring the stabilization of delayed reaction-diffusion networks. Finally, two examples give numerical explanations of the proposed results and highlight the influence of delays.

Stabilization of reaction-diffusion fractional-order memristive neural networks

This paper investigates the stabilization control of fractional-order memristive neural networks with reaction-diffusion terms. With regard to the reaction-diffusion model, a novel processing method based on Hardy-Poincarè inequality is introduced, as a result, the diffusion terms are estimated associated with the information of the reaction-diffusion coefficients and the regional feature, which may be beneficial to obtain conditions with less conservatism. Then, based on Kakutani's fixed point theorem of set-valued maps, new testable algebraic conclusion for ensuring the existence of the system's equilibrium point is obtained. Subsequently, by means of Lyapunov stability theory, it is concluded that the resulting stabilization error system is global asymptotic/Mittag-Leffler stable with a prescribed controller. Finally, an illustrative example about is provided to show the effectiveness of the established results.