Master–slave synchronization of neural networks via event-triggered dynamic controller

Event-triggered protocol-based adaptive impulsive control for delayed chaotic neural networks

This article focuses on the synchronization problem of delayed chaotic neural networks via adaptive impulsive control. An adaptive impulsive gain law in a discrete-time framework is designed. The delay is handled skillfully by using the Lyapunov-Razumikhin method. To improve the flexibility of impulsive control, an event-triggered impulsive strategy to determine when the impulsive instant happens is designed. Additionally, it is proved that the event-triggered impulsive sequence cannot result in the occurrence of Zeno behavior. Some criteria are derived to guarantee synchronization for delayed chaotic neural networks. Eventually, an illustrative example is presented to empirically validate the effectiveness of the suggested strategy.

The Optimization of Control Parameters: Finite-Time Bipartite Synchronization of Memristive Neural Networks With Multiple Time Delays via Saturation Function

This article studies the memristive neural networks with multiple time delays (MNNsMTDs). The topology of networks is signed, which contains both cooperative and competitive relationships. Two controllers without time delays are designed to achieve finite-time bipartite synchronization (FTBS) and practical FTBS (PFTBS) of MNNsMTDs. A novel controller with a saturation function rather than a sign function is proposed to avoid chattering. Along with the Lyapunov function method, some mathematical techniques, and scaling inequalities, some sufficient conditions for FTBS and PFTBS of MNNsMTDs are attained. Besides, this article also concerns fixed-time bipartite synchronization (FXBS) and practical FXBS (PFXBS) of MNNsMTDs. An optimization model is designed to obtain some optimal control parameters. An algorithm based on particle swarm optimization (PSO) is provided to solve this model. Some numerical examples are included to demonstrate the correctness and applicability of the approaches.

H∞ master-slave synchronization for delayed impulsive implicit hybrid neural networks based on memory-state feedback control

This paper investigates the H∞ master-slave synchronization problem for delayed impulsive implicit hybrid neural networks based on memory-state feedback control. By developing a more holistic stochastic impulse-time-dependent Lyapunov-Krasovskii functional and dealing with the nonlinear neuron activation function, the stochastic admissibility and prescribed H∞ performance index for the synchronization error closed-loop system are achieved. In addition, the desired mode-dependent memory-state feedback synchronization controller is acquired in the form of linear matrix inequalities. The free-weighting matrix technique is adopted to remove the inherent limitation of time-varying delay derivative for the implicit delayed systems, and the derivative of time-varying delay is relaxed enough to be greater than 1. The simulation of genetic regulatory network in bio-economic system is given to verify validity of the derived results.

Event-Triggered Quantized Quasisynchronization of Uncertain Quaternion-Valued Chaotic Neural Networks With Time-Varying Delay for Image Encryption

In this article, a class of quaternion-valued master-slave neural networks (NNs) with time-varying delay and parameter uncertainties was first established by conducting the extension from real-valued chaotic NNs to the quaternion field. Then, based on logarithmic quantized output feedback, the quasisynchronization issue of the NNs was investigated via devising a neoteric dynamic event-triggered controller. In virtue of the classical Lyapunov method and a generalized Halanay inequality, not only corresponding synchronization criteria were obtained to realize the quasisynchronization of master-slave NNs but also a precise upper bound was provided. Moreover, Zeno behavior can be eliminated under the presented scheme in this article. The accuracy of the theoretical outcomes was demonstrated by means of Chua's circuit. Ultimately, some experimental results of pragmatic application in image encryption/decryption were exposed to substantiate the feasibility and efficacy of the current algorithm for the proposed quaternion-valued NNs.

A PID controller for synchronization between master-slave neurons in fractional-order of neocortical network model

Modeling of the biological neurons is a way to understand the architecture of neural networks of the brain. A complex brain network includes the synchronization between some groups of neurons. The dynamic behavior of interactions between groups of slave-master neurons in the neocortical network is unpredictable and challenging. The purpose of synchronizing a neural interaction is to reduce the synchronization error between the chaotic slave-master neurons. This paper uses a proportional-integral-derivative (PID) controller to synchronize master-slave neurons in the fractional-order of the neocortical network model based on dendritic spike frequency adaptation (DSFA) uncertainties and unknown disturbance effects. The purpose of this article is in two parts: First, we implemented the effect of previous states of the neuron conditions by fractional-order of the differential equations in the neocortical network model. Second, by synchronizing the FO neocortical master-slave model by PID controller, we investigated the connection strength of the complex network in chaotic point of view. The optimized PID coefficients and fractional-order were calculated using root mean square error (RMSE) criteria to control the membrane voltage synchronization. The chaotic behavior of the system was evaluated by numerical techniques such as attractor analysis and time series diagrams. The optimal RMSE value for master-slave neurons occurred at fractional-orders 0.89. It is shown that the synchronization of master-slave neurons improves over time, and eventually they are fully synchronized while the controller error is reduced.

Event-Triggered State Estimation for Fractional-Order Neural Networks

This paper is concerned with the problem of event-triggered state estimation for a class of fractional-order neural networks. An event-triggering strategy is proposed to reduce the transmission frequency of the output measurement signals with guaranteed state estimation performance requirements. Based on the Lyapunov method and properties of fractional-order calculus, a sufficient criterion is established for deriving the Mittag–Leffler stability of the estimation error system. By making full use of the properties of Caputo operator and Mittag–Leffler function, the evolution dynamics of measured error is analyzed so as to exclude the unexpected Zeno phenomenon in the event-triggering strategy. Finally, two numerical examples and simulations are provided to show the effectiveness of the theoretical results.

Event-based master-slave synchronization of complex-valued neural networks via pinning impulsive control

This paper investigates the synchronization problem of complex-valued neural networks via event-triggered pinning impulsive control (ETPIC). A time-delayed pinning impulsive controller is proposed based on three levels of event-triggered conditions. By employing the Lyapunov functional method and differential inequality technique, sufficient delay-dependent synchronization criteria are derived under the proposed ETPIC scheme. The obtained result shows that synchronization of master and slave complex-valued neural networks can be achieved even if the sizes of delays exceed the length of intervals between any two consecutive impulsive instants determined by Lyapunov-based event-triggered conditions in the proposed control strategy. Moreover, the linear matrix inequality approach is utilized to exclude Zeno behavior. Numerical examples are provided to illustrate the effectiveness of the theoretical results.