Robust Multimode Function Synchronization of Memristive Neural Networks with Parameter Perturbations and Time-Varying Delays

Publisher Copyright: IEEE Copyright: Copyright 2020 Elsevier B.V., All rights reserved.Currently, some works on studying complete synchronization of dynamical systems are usually restricted to its two special cases: 1) power-rate synchronization and 2) exponential synchronization. Therefore, how to give a generalization of these types of complete synchronization by the mathematical expression is an open question that needs to be urgently solved. To begin with, this article proposes multimode function synchronization by the mathematical expression for the first time, which is a generalization of exponential synchronization, power-rate synchronization, logarithmical synchronization, and so on. Moreover, two adaptive controllers are designed to achieve robust multimode function synchronization of memristive neural networks (MNNs) with mismatched parameters and uncertain parameters. Each adaptive controller includes function r(t) and update gain σ. By choosing different types of r(t), multiple types of complete synchronization, including power-rate synchronization and exponential synchronization can be obtained. And update gain σ can be used to adjust the speed of synchronization. Therefore, our results enlarge and strengthen the existing results. Two examples are put forward to verify the validity of our results.Peer reviewedFinal Accepted Versio

Exponential multistability of memristive Cohen-Grossberg neural networks with stochastic parameter perturbations

© 2020 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/.Due to instability being induced easily by parameter disturbances of network systems, this paper investigates the multistability of memristive Cohen-Grossberg neural networks (MCGNNs) under stochastic parameter perturbations. It is demonstrated that stable equilibrium points of MCGNNs can be flexibly located in the odd-sequence or even-sequence regions. Some sufficient conditions are derived to ensure the exponential multistability of MCGNNs under parameter perturbations. It is found that there exist at least (w+2) l (or (w+1) l) exponentially stable equilibrium points in the odd-sequence (or the even-sequence) regions. In the paper, two numerical examples are given to verify the correctness and effectiveness of the obtained results.Peer reviewe

Synchronization of inertial memristive neural networks with time-varying delays via static or dynamic event-triggered control

Funding Information: This work was supported in part by the National Natural Science Foundation of China under Grant 61971185, the Major Research Project of the National Natural Science Foundation of China under Grant 91964108 and the Open Fund Project of Key Laboratory in Hunan Universities under Grant 18K010. Publisher Copyright: © 2020 Elsevier B.V.This paper investigates the synchronization problem of inertial memristive neural networks (IMNNs) with time-varying delays via event-triggered control (ETC) scheme and state feedback controller for the first time. First, two types of state feedback controllers are designed; the first type of controller is added to the transformational first-order system, and the second type of controller is added to the original second-order system. Next, based on each feedback controller, static event-triggered control (SETC) condition and dynamic event-triggered control (DETC) condition are presented to significantly reduce the update times of controller and decrease the computing cost. Then, some sufficient conditions are given such that synchronization of IMNNs with time-varying delays can be achieved under ETC schemes. Finally, a numerical simulation and some data analyses are given to verify the validity of the proposed results.Peer reviewe

Basic control theory for linear fractional differential equations with constant coefficients

In this paper we present an analogous result of the famous Kalman controllability criterion for first order linear ordinary differential equations with constant coefficients that applies to the case of linear differential equations of fractional order with constant coefficients. We use the fractional Gramian matrix, the range space and the Kalman matrix as main tools to derive a sufficient and necessary condition for the controllability of the fractional system. Moreover, we provide some simple examples, including a linear fractional harmonic oscillator, to illustrate our results. Finally, several open problems arising from this topic are suggested, including another simple linear system of incommensurate fractional ordersThis research has been partially supported by the AEI of Spain under Grant MTM2016-75140-P, co-financed by European Community fund FEDER and XUNTA de Galicia under grant ED431C 2019/02. Sebastián Buedo-Fernández also acknowledges current funding from Ministerio de Educación, Cultura y Deporte of Spain (FPU16/04416) and previous funding from Xunta de Galicia (ED481A-2017/030)S

Multisynchronization for Coupled Multistable Fractional-Order Neural Networks via Impulsive Control

We show that every subnetwork of a class of coupled fractional-order neural networks consisting of N identical subnetworks can have r+1n locally Mittag-Leffler stable equilibria. In addition, we give some algebraic criteria for ascertaining the static multisynchronization of coupled fractional-order neural networks with fixed and switching topologies, respectively. The obtained theoretical results characterize multisynchronization feature for multistable control systems. Two numerical examples are given to verify the superiority of the proposed results