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

Weighted Sum Synchronization of Memristive Coupled Neural Networks

Funding Information: This work is supported by the National Natural Science Foundation of China (No. 61971185) and the Open Fund Project of Key Laboratory in Hunan Universities (No. 18K010). Publisher Copyright: © 2020 Elsevier B.V.It is well known that weighted sum of node states plays an essential role in function implementation of neural networks. Therefore, this paper proposes a new weighted sum synchronization model for memristive neural networks. Unlike the existing synchronization models of memristive neural networks which control each network node to reach synchronization, the proposed model treats the networks as dynamic entireties by weighted sum of node states and makes the entireties instead of each node reach expected synchronization. In this paper, weighted sum complete synchronization and quasi-synchronization are both investigated by designing feedback controller and aperiodically intermittent controller, respectively. Meanwhile, a flexible control scheme is designed for the proposed model by utilizing some switching parameters and can improve anti-interference ability of control system. By applying Lyapunov method and some differential inequalities, some effective criteria are derived to ensure the synchronizations of memristive neural networks. Moreover, the error level of the quasi-synchronization is given. Finally, numerical simulation examples are used to certify the effectiveness of the derived results.Peer reviewe

SATURATED AND ASYMMETRIC SATURATED IMPULSIVE CONTROL SYNCHRONIZATION OF COUPLED DELAYED INERTIAL NEURAL NETWORKS WITH TIME-VARYING DELAYS

This paper considers control systems with impulses that are saturated and asymmetrically saturated which are used to examine the synchronization of inertial neural networks (INNs) with time-varying delay and coupling delays. Under the theoretical discussions, mixed delays, such as transmission delay and coupling delay are presented for inertial neural networks. The addressed INNs are transformed into first order differential equations utilizing variable transformation on INNs and then certain adequate conditions are derived for the exponential synchronization of the addressed model by substituting saturation nonlinearity with a dead-zone function. In addition, an asymmetric saturated impulsive control approach is given to realize the exponential synchronization of addressed INNs in the leader-following synchronization pattern. Finally, simulation results are used to validate the theoretical research findings

Synchronization analysis of coupled fractional-order neural networks with time-varying delays

In this paper, the complete synchronization and Mittag-Leffler synchronization problems of a kind of coupled fractional-order neural networks with time-varying delays are introduced and studied. First, the sufficient conditions for a controlled system to reach complete synchronization are established by using the Kronecker product technique and Lyapunov direct method under pinning control. Here the pinning controller only needs to control part of the nodes, which can save more resources. To make the system achieve complete synchronization, only the error system is stable. Next, a new adaptive feedback controller is designed, which combines the Razumikhin-type method and Mittag-Leffler stability theory to make the controlled system realize Mittag-Leffler synchronization. The controller has time delays, and the calculation can be simplified by constructing an appropriate auxiliary function. Finally, two numerical examples are given. The simulation process shows that the conditions of the main theorems are not difficult to obtain, and the simulation results confirm the feasibility of the theorems

New criteria on global Mittag-Leffler synchronization for Caputo-type delayed Cohen-Grossberg Inertial Neural Networks

Our focus of this paper is on global Mittag-Leffler synchronization (GMLS) of the Caputo-type Inertial Cohen-Grossberg Neural Networks (ICGNNs) with discrete and distributed delays. This model takes into account the inertial term as well as the two types of delays, which greatly reduces the conservatism with respect to the model. A change of variables transforms the $2\beta$ order inertial frame into $\beta$ order ordinary frame in order to deal with the effect of the inertial term. In the following steps, two novel types of delay controllers are designed for the purpose of reaching the GMLS. In conjunction with the novel controllers, utilizing differential mean-value theorem and inequality techniques, several criteria are derived to determine the GMLS of ICGNNs within the framework of Caputo-type derivative and calculus properties. At length, the feasibility of the results is further demonstrated by two simulation examples

Mittag–Leffler synchronization for impulsive fractional-order bidirectional associative memory neural networks via optimal linear feedback control

In this paper, we are concerned with the synchronization scheme for fractional-order bidirectional associative memory (BAM) neural networks, where both synaptic transmission delay and impulsive effect are considered. By constructing Lyapunov functional, sufficient conditions are established to ensure the Mittag–Leffler synchronization. Based on Pontryagin’s maximum principle with delay, time-dependent control gains are obtained, which minimize the accumulative errors within the limitation of actuator saturation during the Mittag–Leffler synchronization. Numerical simulations are carried out to illustrate the feasibility and effectiveness of theoretical results with the help of the modified predictor-corrector algorithm and the forward-backward sweep method

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

Synchronization for discrete coupled fuzzy neural networks with uncertain information via observer-based impulsive control

This paper discussed the synchronization of impulsive fuzzy neural networks (FNNs) with uncertainty of information exchange. Since the data of neural networks (NNs) cannot be completely measured in reality, we designed an observer-based impulsive controller on the basis of the partial measurement results and achieved the purpose of reducing the communication load and the controller load of FNNs. In terms of the Lyapunov stability theory, an impulsive augmented error system (IAES) was established and two sufficient criteria to guarantee the synchronization of our FNNs system were obtained. Finally, we demonstrated the validity of the results by a numerical example

A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing

This work introduces a three-dimensional, highly nonlinear quadratic oscillator with no linear terms in its equations. Most of the quadratic ordinary differential equations (ODEs) such as Chen, Rossler, and Lorenz have at least one linear term in their equations. Very few quadratic systems have been introduced and all of their terms are nonlinear. Considering this point, a new quadratic system with no linear term is introduced. This oscillator is analyzed by mathematical tools such as bifurcation and Lyapunov exponent diagrams. It is revealed that this system can generate different behaviors such as limit cycle, torus, and chaos for its different parameters' sets. Besides, the basins of attractions for this system are investigated. As a result, it is revealed that this system's attractor is self-excited. In addition, the analog circuit of this oscillator is designed and analyzed to assess the feasibility of the system's chaotic solution. The PSpice simulations confirm the theoretical analysis. The oscillator's time series complexity is also investigated using sample entropy. It is revealed that this system can generate dynamics with different sample entropies by changing parameters. Finally, impulsive control is applied to the system to represent a possible solution for stabilizing the system