Quasisynchronization of Discrete-Time Inertial Neural Networks With Parameter Mismatches and Delays

Heterogeneous boundary synchronization of time-delayed competitive neural networks with adaptive learning parameter in the space-time discretized frames

This article presents the master-slave time-delayed competitive neural networks in space-time discretized frames(STD-CNNs) with the heterogeneous structure, induced by the design of an adaptive learning parameter in the slave STD-CNNs. This article addresses the issue of exponential synchronization for the time-delayed STD-CNNs with the heterogeneous structure via the controls at the boundaries, based on the learning law setting for the parameter in the slave STD-CNNs. In a corresponding manner, the exponential synchronization for time-delayed STD-CNNs with the homogeneous structure can be achieved via boundary controls. This study demonstrates that the problem of exponential synchronization for time-delayed heterogeneous STD-CNNs can be modeled by designating a time-varying learning parameter in the slave STD-CNNs, which can then be solved by means of calculative linear matrix inequalities(LMIs). To illustrate the feasibility of the current work, a numerical example is presented.

Event-Triggered Output-Feedback Control for Synchronization of Delayed Neural Networks

This article proposes a novel discrete event-triggered scheme (DETS) for the synchronization of delayed neural networks (NNs) using the dynamic output-feedback controller (DOFC). The proposed DETS uses both the current and past samples to determine the next trigger, unlike the traditional event-triggered scheme (ETS) that uses only the current sample. The proposed DETS is employed in a dual setup for two network channels to significantly reduce redundant data transmission. A DOFC is designed to achieve the synchronization of the NNs. Stability criteria of the synchronisation error system are derived based on the Lyapunov-Krasovskii functional method, and the co-design of the DOFC and DETS parameters are accomplished using the Cone-complementarity linearization (CCL) approach. The effectiveness and advantages of the proposed method are illustrated considering an example of the chaotic system.

Master-Slave Synchronization of Neural Networks With Unbounded Delays via Adaptive Method

Master-slave synchronization of two delayed neural networks with adaptive controller has been studied in recent years; however, the existing delays in network models are bounded or unbounded with some derivative constraints. For more general delay without these restrictions, how to design proper adaptive controller and prove rigorously the convergence of error system is still a challenging problem. This article gives a positive answer for this problem. By means of the stability result of unbounded delayed system and some analytical techniques, we prove that the traditional centralized adaptive algorithms can achieve global asymptotical synchronization even if the network delays are unbounded without any derivative constraints. To describe the convergence speed of the synchronization error, adaptive designs depending on a flexible ω -type function are also provided to control the synchronization error, which can lead exponential synchronization, polynomial synchronization, and logarithmically synchronization. Numerical examples on delayed neural networks and chaotic Ikeda-like oscillator are presented to verify the adaptive designs, and we find that in the case of unbounded delay, the intervention of ω -type function can promote the realization of synchronization but may destroy the convergence of control gain, and this however will not happen in the case of bounded delay.

Intermittent Control for Quasisynchronization of Delayed Discrete-Time Neural Networks

This article visits the intermittent quasisynchronization control of delayed discrete-time neural networks (DNNs). First, an event-dependent intermittent mechanism is originally designed, which is described by the Lyapunov function and three non-negative real regions. The distinctive feature is that the controller starts to work only when the trajectory of the Lyapunov function goes into the presupposed work region. The proposed method fundamentally changes the principle of the existing intermittent control schemes. Under the proposed framework of the intermittent mechanism, the work/rest time of the controller is aperiodic, unpredictable, and initial value dependent. Second, several succinct sufficient conditions in terms of linear matrix inequalities are developed to achieve the quasisynchronization of the considered DNNs. A simple optimization algorithm is established to compute the control gains and the Lyapunov matrices such that synchronization error is stabilized to the smallest convergence region. Finally, two simulation examples are provided to demonstrate the feasibility of the designed intermittent mechanism.

Stability of delayed inertial neural networks on time scales: A unified matrix-measure approach

This note introduces a unified matrix-measure concept to study the stability of a class of inertial neural networks with bounded time delays on time scales. The novel matrix-measure concept unifies the classic matrix-measure and the generalized matrix-measure concept. One sufficient global exponential stability criterion is obtained based on this key matrix-measure and no Lyapunov function is required. To make the stability performance better, another stability criterion in which more detailed information is involved has been acquired. The theoretical results in this note contain and extend some existing continuous-time and discrete-time works. A numerical example is given to show the validity of the results.