Finite-Time Lag Synchronization of Memristive Neural Networks With Multi-Links via Adaptive Control

Abstract

The finite-time lag synchronization problem of memristive neural networks with multi-links (MNNLs) is discussed with the adaptive controllers, and the discrete and distributed time-varying delays are included in the network models. With the Lyapunov functional method and the properties of inequality, two different finite-time methods are adopted to prove and compare the effects of the two proposed theorems, and three corollaries are obtained and to be analyzed. Using the assumptions of Lipschitz continuous and boundedness of the activation functions, three lemmas are derived to deal with the difficulty caused by the memristive jumping properties and synchronization lag feature, which make the proof of the theorems simple and clear. Based on that whether time-varying delays are included, with the adaptive control strategy, we design delay-independent and delay-dependent adaptive controllers with different adaptive parameters for the MNNLs respectively. Finally, two numerical simulations are given to show the effectiveness and correctness of the obtained theoretical results. INDEX TERMS Memristive neural networks with multi-links, finite-time lag synchronization, delaydependent adaptive control, delay-independent adaptive control, distributed time-varying delays.

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

“…MNNs have the capability of memory, adaptability, and highly parallel processing. Memristors and neuronal synapses have similar characteristics [5]. There are three main synaptic links: a dendrite-axon synapse, a soma-axon synapse, and an axon-axon synapse [6].…”

“…Generally, the ST of FTS depends on the initial values of the systems, whereas the ST of fixed-time synchronization (FXS) is irrelevant to the initial values of the systems. A usual method is to design a controller using the sign function [5], [6], [20], [21] to realize FTS or FXS. However, the use of the sign function could lead to undesired chattering.…”

“…The authors also studied the BS of inertia MNNs in [30]. Qin et al [5] investigated lag FTS of MNNs with multi-links. FTBS for fractional-order impulsive networks was studied in [31].…”

“…Since different synapses are linked in different ways, which causes different transmission delays, that is why multiple time delays are introduced in this article. 2) Different from single FTS [5] or BS [30], FTBS is studied in this article. That is to say, the topology of the networks is signed, which contains both cooperative and competitive relationships.…”

“…3) Two controllers are designed with the sign function and the saturation function to achieve FTBS and PFTBS, respectively. Most articles [1], [5], [15] designed a controller with sign function to achieve FTS. However, it is easy to cause chatting.…”