Adaptive outer synchronization and topology identification between two complex dynamical networks with time-varying delay and disturbance

Abstract

In this paper, we investigate adaptive outer synchronization for identifying unknown network topology and parameters between two coupled complex networks with time-varying delays existing in the node dynamics and coupling forms. By designing adaptive controllers and updating laws, we obtain two theorems on the appearance of outer synchronization using Lyapunov stability theory. In the numerical examples, we provide the detailed identification criteria of network topology and system parameter according to the obtained theorems and give some numerical examples to show the efficiency of the proposed controllers.

Outer Synchronization of a Modified Quorum-Sensing Network via Adaptive Control

“…. , , then the synthetic gene network (5)- (7) with controllers (23) and estimations (12) can achieve outer synchronization.…”

“…The former can be employed to discuss local stability of the synchronous state, and the latter can be used to explore global stability of the synchronous state. Up to now, dozens of different types of synchronization states have been proposed such as complete synchronization [14], cluster synchronization [15,16], lag synchronization [17,18], projection synchronization [19,20], and outer synchronization [21][22][23]. Thereinto, outer synchronization has attracted many researchers' interest, which describes the synchronization 2 Mathematical Problems in Engineering between two or more networks.…”

“…Recently, outer synchronization of the fractional order node dynamics was considered in [21], and outer synchronization under aperiodically adaptive intermittent control was considered in [22]. In many cases, networks can not realize a certain expected synchronization relying on just coupling interaction between different nodes [23]. Therefore, many different kinds of output control methods have been introduced, such as pinning control [25], sliding mode control [26,27], adaptive control [28,29], and state feedback control [30].…”

Graph-theoretic method on topology identification of stochastic multi-weighted complex networks with time-varying delayed coupling and non-delayed coupling

“…Therefore, it is very meaningful and practical to consider time delay into the problem about topology identification. Among the existing work, topology identification of complex networks with time delay has drawn considerable attention and obtained many useful results [17,18,19,20,21,22,23,24,25]. It is worth noting that time delay is usually a constant in existing researches on topology identification of complex networks, see [17,18,19,20,21,22,23].…”

Parameter Identification and Adaptive Control of Uncertain Goodwin Oscillator Networks with Disturbances

“…Under the effects of these uncertainties, the achieved synchronization might be destroyed and broken. Therefore, it is necessary to design an adaptive control law that adapts itself to these uncertainties, which is a popular control technique used for complex network models with unknown parameters [28][29][30]. The theoretical basis of adaptive control is parameter identification.…”