Finite-Time Projective Lag Synchronization and Identification between Multiple Weights Markovian Jumping Complex Networks with Stochastic Perturbations

Abstract

Two nonidentical dimension Markovian jumping complex networks with stochastic perturbations are taken as objects. e network models under two conditions including single weight and double weights are established, respectively, to study the problem of synchronization and identification. A finite-time projection lag synchronization method is proposed and the unknown parameters of the network are identified. First of all, based on Itô's formula and the stability theory of finite-time, a credible finite-time adaptive controller is presented to guarantee the synchronization of two nonidentical dimension Markovian jumping complex networks with stochastic perturbations under both conditions. Meanwhile, in order to identify the uncertain parameters of the network with stochastic perturbations accurately, some corresponding sufficient conditions are given. Finally, numerical simulations under two working conditions are given to demonstrate the effectiveness and feasibility of the main theory result.Hindawi Complexity Volume 2020, Article ID 9713652, 25 pages https://doi.org/10.1155/2020/9713652 networks, an effective approach is adopting finite-time control methods. In addition, as an important factor, stochastic perturbations will ineluctably affect the dynamical of the complex network and even destroy the stability of the system in some kinds of practical situations [9][10][11]. erefore, in complex dynamical networks, both the stochastic perturbations and how to achieve finite-time synchronization cannot be ignored. Withal, at reality operation conditions, the topology of the network would be randomly switched over time [12,13]. To this end, a Markovian process is introduced to describe. Because of the powerful mathematical modeling ability of the Markovian process in many situations, this kind of network has been developed and studied promptly.At the meantime, in many complex network synchronization research studies, the system parameters are known. In [14], the asymptotic synchronization of complex networks with nonlinear nodes of different dimensions is studied, but the parameters of the node system are known. However, this situation is not sufficient in the process of practical.