Synchronization of coupled neural networks under mixed impulsive effects: A novel delay inequality approach

Synchronization of Neural Networks Involving Distributed-Delay Coupling: A Distributed-Delay Differential Inequalities Approach

In this article, we address the synchronization issue for coupled neural networks (CNNs) with mixed couplings by way of the delayed impulsive control, where the delay is distributed. Particularly, mixed couplings comprise the current-state coupling and the distributed-delay coupling, where influences on network connections caused by the past information of CNNs over a certain period are considered. First, we propose a novel array of delayed impulsive differential inequalities involving distributed-delay-dependent impulses, where distributed delays can be relatively larger. Second, we apply such delayed inequalities to analyze the problem of synchronization for CNNs with two different topologies. Sufficient criteria and distributed-delay-dependent impulsive controller are derived thereby. Furthermore, using techniques of matrix decomposition, several low-dimensional criteria are set out, which are appropriate for applications of large scale CNNs. Finally, a numerical example of CNNs with both the current-state coupling and the distributed-delay coupling involving three cases, are exhibited to exemplify the validity and the efficiency of the obtained theoretical results.

Exponential synchronization of delayed coupled neural networks with delay-compensatory impulsive control

This paper studies the exponential synchronization problem for a class of delayed coupled neural networks with delay-compensatory impulsive control. A Razumikhin-type inequality involving some destabilizing delayed impulse gains and a new idea of delay-compensatory that shows two critical roles for system stability are presented, respectively. Based on the constructed inequality and the presented delay-compensatory idea, sufficient stability and synchronization criteria for globally exponential synchronization (GES) of coupled neural networks (CNNs) are presented. Compared with existing results, the uniqueness of the presented results lies in that impulse delays can be fetched and integrated to compensate for instantaneous unstable impulse dynamics caused by destabilizing gains. Moreover, constraints between system delay and impulsive delay are relaxed, and the interval of impulses no longer constrains the system delay. Comparisons and a practical application are given to demonstrate the superior performance of the presented novel control methods.

Local Synchronization of Directed Lur'e Networks With Coupling Delay via Distributed Impulsive Control Subject to Actuator Saturation

This article studies the local exponential synchronization synthesis problem of directed Lur'e networks with coupling time-varying delay under the distributed impulsive control subject to actuator saturation. First, by utilizing proof by contradiction, impulsive comparison principle, and latest improved convex hull representation of saturation function, some delay-independent sufficient criteria for local exponential synchronization are presented in the form of bilinear matrix inequalities. Meanwhile, a novel method with less conservatism is developed to estimate the domain of attraction, which is radically different from the traditional method by means of contractive invariant set. Second, optimization problems constrained by the transformed linear matrix inequalities are established to acquire the maximum estimates of both the domain of attraction and average impulsive interval (AII), which are conveniently solved by the YALMIP toolbox in MATLAB software. Finally, a numerical simulation is rendered to demonstrate the effectiveness and advantages of the proposed theoretical results.

Synchronization of coupled switched neural networks subject to hybrid stochastic disturbances

In this paper, the theoretical analysis on exponential synchronization of a class of coupled switched neural networks suffering from stochastic disturbances and impulses is presented. A control law is developed and two sets of sufficient conditions are derived for the synchronization of coupled switched neural networks. First, for desynchronizing stochastic impulses, the synchronization of coupled switched neural networks is analyzed by Lyapunov function method, the comparison principle and a impulsive delay differential inequality. Then, for general stochastic impulses, by partitioning impulse interval and using the convex combination technique, a set of sufficient condition on the basis of linear matrix inequalities (LMIs) is derived for the synchronization of coupled switched neural networks. Eventually, two numerical examples and a practical application are elaborated to illustrate the effectiveness of the theoretical results.

Input-to-State Stability of Nonlinear Impulsive Systems Subjects to Actuator Saturation and External Disturbance

This article mainly explores the local input-to-state stability (LISS) property of a class of nonlinear systems via a saturated control strategy, where both the external disturbance and impulsive disturbance being fully considered. In terms of the Lyapunov method and inequality techniques, some sufficient conditions under which the system can be made LISS are proposed, and the elastic constraint relationship among saturated control gain, rate coefficients, external disturbance, and domain of initial value is revealed. Moreover, the optimization design procedures are provided with the hope of obtaining the estimates of admissible external disturbance and domain of initial value as large as possible, where the corresponding saturated control law can be designed by solving LMI -based conditions. In the absence of an external disturbance, the locally exponential stability (LES) property can also be presented with a set of more relaxed conditions. Finally, two examples are presented to reveal the validity of the obtained results.

Cluster synchronization of delayed coupled neural networks: Delay-dependent distributed impulsive control

This paper investigates the issue of cluster synchronization (CS) for the coupled neural networks (CNNs) with time-varying delays via the delay-dependent distributed impulsive control. A new Halanay-like inequality, where delayed impulses are taken into consideration, is proposed. Based on the Lyapunov theory and the new differential inequality, sufficient conditions of CS for delayed CNNs with fixed and switching coupling topology are obtained, respectively. Moreover, delay-dependent distributed impulsive controllers with fixed or switching topology are designed thereby. Finally, we present a numerical example of CNNs with fixed or switching coupling to verify the effectiveness of our results, respectively.

Synchronization for stochastic coupled networks with Lévy noise via event-triggered control

This paper addresses the realization of almost sure synchronization problem for a new array of stochastic networks associated with delay and Lévy noise via event-triggered control. The coupling structure of the network is governed by a continuous-time homogeneous Markov chain. The nodes in the networks communicate with each other and update their information only at discrete-time instants so that the network workload can be minimized. Under the framework of stochastic process including Markov chain and Lévy process, and the convergence theorem of non-negative semi-martingales, we show that the Markovian coupled networks can achieve the almost sure synchronization by event-triggered control methodology. The results are further extended to the directed topology, where the coupling structure can be asymmetric. Furthermore, we also proved that the Zeno behavior can be excluded under our proposed approach, indicating that our framework is practically feasible. Numerical simulations are provided to demonstrate the effectiveness of the obtained theoretical results.

Stochastic quasi-synchronization of heterogeneous delayed impulsive dynamical networks via single impulsive control

This paper investigates the quasi-synchronization problem of the stochastic heterogeneous complex dynamical networks with impulsive couplings and multiple time-varying delays. It is shown that this kind of dynamical networks can achieve exponential quasi-synchronization by exerting impulsive control added on only one chosen pinning node. By employing the Lyapunov stability theory, some sufficient criteria on quasi-synchronization for this dynamical network are established, revealing the relationship between the quasi-synchronization performance and the stochastic perturbations as well as the frequency and strength of impulsive coupling. Finally, some numerical examples are used to illustrate the effectiveness of the main results.

Synchronization criteria of delayed inertial neural networks with generally Markovian jumping

In this paper, the synchronization problem of inertial neural networks with time-varying delays and generally Markovian jumping is investigated. The second order differential equations are transformed into the first-order differential equations by utilizing the variable transformation method. The Markovian process in the systems is uncertain or partially known due to the delay of data transmission channel or the loss of data information, which is more general and practicable to consider generally Markovian jumping inertial neural networks. The synchronization criteria can be obtained by using the delay-dependent Lyapunov-Krasovskii functionals and higher order polynomial based relaxed inequality (HOPRII). In addition, the desired controllers are obtained by solving a set of linear matrix inequalities. Finally, the numerical examples are provided to demonstrate the effectiveness of the theoretical results.