Fuzzy-Based Impulsive Synchronization of Different Complex Networks with Switching Topology and Time-Varying Dynamic
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Fuzzy-Based Impulsive Synchronization of Different Complex Networks with Switching Topology and Time-Varying Dynamic Reza Behinfaraz1 • Sehraneh Ghaemi1 • Sohrab Khanmohammadi1 Mohammad Ali Badamchizadeh1
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Received: 25 November 2019 / Revised: 3 July 2020 / Accepted: 23 August 2020 Taiwan Fuzzy Systems Association 2020
Abstract In this paper, the synchronization problem of complex networks using fuzzy-based impulsive control is discussed. Synchronization problem is considered for networks with switching topologies. Also, each node of the networks has a time-varying chaotic dynamic. Based on the Takagi–Sugeno fuzzy model, a new representation of a complex network is presented. Using impulsive control theory, a new controller for the synchronization of timevarying networks is designed. The synchronization problem has been extended for two different networks. Simulation examples show the effectiveness of the proposed method. Keywords Synchronization Complex network Switching topology Impulsive control Fuzzy logic
& Sehraneh Ghaemi [email protected] Reza Behinfaraz [email protected] Sohrab Khanmohammadi [email protected] Mohammad Ali Badamchizadeh [email protected] 1
Department of Control Engineering, Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran
1 Introduction According to the past applications of complex networks, attention to these networks is growing every day, and analyzing different types of these networks has become state of the art in many fields [1–3]. Synchronization of complex networks is a challenging problem since it has a wide variety of applications in different fields [4, 5]. Synchronization problem is defined in different types according to practical requirements and constraints [6, 7]. Different methods have been introduced for the synchronization of complex networks such as [8–10]. One of the used methods for synchronization of complex networks is the impulsive control method [11]. Impulsive control method is a discrete time control method [12, 13]. Compared to others, impulsive control has many advantages. To mention the most distinct one, the convergence rate of this method is far higher than the others. Moreover, impulsive control requires less control effort compared to other prevalent methods. In [14, 15], synchronization problems are studied with different methods and network modeling, however, the considered complex networks are with constant links. In many real-world applications of complex networks, due to different reasons such as failure of a link, the links between nodes can vanish or emerge [16, 17]. To the best of our knowledge, synchronization problem for two different complex networks based on impulsive control has not been done yet. Especially, for the networks with switching topology, there are no specific study. Then, we work on an impulsive controller which has the ability of synchronization of two different networks with switching topology. In this paper, a new type of modeling is introduced due to the nonli
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