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Finite-time structure identification and synchronization of drive-response systems with uncertain parameter

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Abstract

This paper proposes an approach of finite-time synchronization to identify the topological structure and unknown parameters simultaneously for under general complex dynamical networks. Based on the finite-time stability theory, an effective control input and a feedback control with an updated law are designed to realize finite-time synchronization between two complex networks. The unknown network topological structure and system parameters of uncertain general complex dynamical networks are identified simultaneously. Since finite-time topology identification means the suboptimum in identified time, the results of this paper are important. Several useful criteria for finite-time synchronization are given. Finally, two examples simulations for supporting the theoretical results are also provided.

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... Besides, for the research of uncertain parameters in a finite time, a class of Markovian jump complex networks with partially unknown transition rates is also considered to achieve the finite-time stability or synchronization characteristics of systems [34][35][36]. Mei et al. [41,42] study the finite-time topological identification and synchronization of drive-response (master-slave) system based on an effective control input and a feedback control with an updated law respectively. Wang et al. [43] investigates finite-time synchronization and parameter identification problem for uncertain Lurie systems based on the finite-time stability theory and the adaptive control method. ...
... are any vectors and q 0 < < 2 is a real number satisfying: Remark 1. Some works have been done in the finite-time topological identification and synchronization simultaneously for complex network [41,42], they could not consider the effect of external environment and multiple time delays. Therefore, in the next two sections, we consider external environment and multiple time delays, and the issues of finitetime topological identification for complex network with the same and different topological structure are studied respectively. ...
... Remark 3. In the previous researches, some results were obtained in parameters identification and structure identification, including asymptotic topological identification [37][38][39][40], exponential asymptotic parameters identification [1] and finite-time parameters identification [41][42][43]. However, they consider structure identification in the complex network with the same topological structure. ...
... Reference [20] solved the robust finite-time synchronization of an uncertain Markovian complex dynamic network with time-varying delay and reaction-diffusion terms. By designing a feedback controller with update law, Mei [21] evaluated a class of finite-time synchronization problems of a drive-response system that can identify topology structure and uncertain parameters simultaneously and obtained a sufficient condition that can ensure a system to achieve synchronization. ...
... Reference [20] discussed a neural network. For the system model studied in Ref. [21], the internal coupling relationship is linear, which is different from our model and method. Reference [25] evaluated the cluster synchronization of a fuzzy complex network. ...
... For systems without uncertainty, such as model (15), system instability may occur given the changes in controller parameters. Here, we investigate the finite-time synchronization problem of system (15) by using a non-fragile controller (21). (15), under Assumptions 1 and 2, if positive-definite symmetric matrices K i , P i , S i and Q i exist, so that ...
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Abstract This study investigates the finite-time synchronization of uncertain nonlinear complex dynamic networks with time-varying delay. For a class of complex network models with time-varying delay and uncertain system parameters, the time delay changes infrequently, uncertain terms are unknown but bounded, and the matching conditions are satisfied. The coupling relationship between nodes is a nonlinear function with time delay, and the function satisfies the Lipschitz condition. A new criterion for the finite-time synchronization of a class of complex dynamical networks with variable delay is obtained, and the upper bound of the time for the system to achieve synchronization is presented by constructing a suitable Lyapunov–Krasovskii function, designing a nonlinear controller, and combining analysis techniques, such as matrix inequality. Finally, the validity of finite-time synchronization is verified through computer simulation.
... Besides, for the research of uncertain parameters in a finite time, a class of Markovian jump complex networks with partially unknown transition rates is also considered to achieve the finite-time stability or synchronization characteristics of systems [34][35][36]. Mei et al. [41,42] study the finite-time topological identification and synchronization of drive-response (master-slave) system based on an effective control input and a feedback control with an updated law respectively. Wang et al. [43] investigates finite-time synchronization and parameter identification problem for uncertain Lurie systems based on the finite-time stability theory and the adaptive control method. ...
... are any vectors and q 0 < < 2 is a real number satisfying: Remark 1. Some works have been done in the finite-time topological identification and synchronization simultaneously for complex network [41,42], they could not consider the effect of external environment and multiple time delays. Therefore, in the next two sections, we consider external environment and multiple time delays, and the issues of finitetime topological identification for complex network with the same and different topological structure are studied respectively. ...
... Remark 3. In the previous researches, some results were obtained in parameters identification and structure identification, including asymptotic topological identification [37][38][39][40], exponential asymptotic parameters identification [1] and finite-time parameters identification [41][42][43]. However, they consider structure identification in the complex network with the same topological structure. ...
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This paper investigates issues of finite-time topological identification and stochastic synchronization for two complex networks with multiple time delays. In the paper, we propose two different approaches to identify the topological structure and guarantee stochastic synchronization for complex networks in finite time, which are achieved based on finite-time stability theory and properties of Wiener process. Several useful finite-time synchronization and identification criteria are obtained simultaneously based on adaptive feedback control method. In the final section, numerical examples are examined to illustrate the effectiveness of the analytical results.
... Siamak Heidarzadeh heidarzadehsiamak@yahoo.com there still do not exist such control schemes for synchronization of general class of multi-input multi-output master and slave chaotic systems. Another important issue in designing synchronization control schemes for chaotic systems is the optimality in settling time or finite-time convergence of errors to zero (Li and Tian 2003;Mei et al. 2013;Wang et al. 2009;Chen et al. 2014). This optimality is especially important in secure communication and data encryption systems (Kwon et al. 2011;Yang et al. 1997;Liu et al. 2016), which are important applications of chaos synchronization. ...
... For example, Li and Tian (2003) presented an active control scheme for finite-time synchronization of chaotic systems. Mei et al. (2013) used adaptive finite-time control to design synchronization control scheme. Chen et al. (2014) designed a new controller called the generalized variable substitution control method to synchronize two Lorenz-Stenflo in finite time. ...
... Since ksk 1 ! ksk (Mei et al. 2013), (28) is simplified to: ...
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... [18][19][20] Although parameter estimation is not the main purpose of the synchronization methods, it turns out that, for certain dynamical systems, they can be efficiently used for online identification of unknown parameters as well. [21][22][23] However, despite their partial success in several engineering fields, they are still in the early stages for civil and structural engineering problems. In particular, from a structural designer's point of view, an ideal online identification method should consider the following matters. ...
... Next, we substitute (28) and (30) into (21) to get (54), which is equal to H * 1 defined in (52). ...
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... In [7], the author put forward passivity of directed and undirected complex dynamical networks with adaptive coupling weights. Mei et al. [20] investigated finite-time synchronization and parameter identification problem for drive-response dynamical networks with unknown network topological structure and system parameters based on the finite-time stability theory and the adaptive control method. By making use of finite-time stability theory and properties of Wiener process, finite-time topological identification and stochastic synchronization for two complex networks with multiple time delays were obtained in [21]; in addition, Zhao et al. studied finitetime topology identification and stochastic synchronization of complex network with multiple time delays. ...
... , sign( ( ))) , 0 < < 1, and is an adjusted constant. With the help of the update law design in [20], the adaptive parameter ( ), = 1, 2, . . . , , is as follows:̇( ...
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... Zhang and Han [30] researched the finite-time synchronization of uncertain complex networks with nonidentical nodes on the basis of special unilateral coupling control; however, the method requires the estimation of uncertain parameters and the assumption of a topology that satisfies conditions automatically. Mei et al. [31] discussed a class of finite-time synchronization for drive-response systems with structure identification and uncertain parameters. Xu et al. [32] studied the finite-time synchronization of Markovian jump complex networks with generally uncertain transition rates. ...
... Zhao et al. [34] obtained new results on finite-time parameter identification and synchronization of uncertain complex dynamic networks with perturbations and impulsive effects on the basis of the finite time stability theorem, in which a system's uncertainty is caused by uncertain parameters. Moreover, in [31][32][33][34], the nonlinearity of the internal coupling of systems was not considered. Sun et al. [35] realized the finite-time synchronization of complex chaotic systems with three unknown parameter terms by means of sliding mode control. ...
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... In [56], finite-time synchronization of general complex networks with time-varying delays and hybrid couplings was studied by designing a simple discontinuous state feedback controller. Mei et al. [57] explore the finite-time synchronization in drive-response dynamical networks with non-delay coupling and the response networks has uncertain parameter by feedback control and an updated law. Periodically intermittent control was designed to achieve finite-time synchronization of complex dynamical networks with time-varying delay [58], [59]. ...
... Remark 3.10: When the model does not contain unknown parameters and external disturbances, then finite-time lag synchronization of networks was discussed in [60], [61] by utilizing adaptive error-feedback control and intermittent sliding mode control respectively. Remark 3.11: When the network model has no external disturbances and the propagation delay coupling τ (t) = 0, then finite-time synchronization in drive-response complex dynamical network was discussed in [57] by adaptive control. ...
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... In addition, some previous work views the finite-time synchronization via intermittent control in [30], which will be extended in this paper. Besides, many superiority in finite-time stability has no emphasis in this paper (see [30][31][32]). ...
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... In practical physical systems, the parameters of chaotic systems may not be known exactly. So, there are many papers concerning uncertain chaotic systems [1,2]. For the character of the uncertain chaotic systems, many significant results have been obtained by using adaptive control technique, for example, output feedback control [3], fuzzy adaptive control [4], and optimal control [5]. ...
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... Outer synchronization between drive and response networks via adaptive impulsive pinning control is investigated in [31]. An effective control input and a feed-back control with an updated law are designed to realize finite-time synchronization between two complex networks [32] . Among the various works of synchronization, continuoustime synchronization [11−14] and discrete-time synchronization [15][16][17]34] cases are studied respectively. ...
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... The finite-time synchronization has been investigated to identify all the unknown parameters for two coupled neural networks with time delay [31]. An approach of finite-time synchronization has been adopted to identify the topological structure and unknown parameters simultaneously for general complex dynamical networks [32]. The exponential and finite-time synchronization are investigated to realize parameters identification for uncertain multilinks complex network by using the impulsive control method [33]. ...
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... Up to now, many synchronization methods are developed. [7][8][9][10][11][12][13][14][15][16][17][18][19][20] Recently, generalized variable projective synchronization has been investigated. 21 In this paper, author research generalized variable projective synchronization between two unified time delayed systems with constant and modulated time delays. ...
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The study of networks pervades all of science, from neurobiology to statistical physics. The most basic issues are structural: how does one characterize the wiring diagram of a food web or the Internet or the metabolic network of the bacterium Escherichia coli? Are there any unifying principles underlying their topology? From the perspective of nonlinear dynamics, we would also like to understand how an enormous network of interacting dynamical systems-be they neurons, power stations or lasers-will behave collectively, given their individual dynamics and coupling architecture. Researchers are only now beginning to unravel the structure and dynamics of complex networks.
We study synchronization and desynchronization of a complex network of chaotic dynamical systems, in both continuous-time and discrete-time cases. With proved synchronization conditions, we illustrate network synchronization and desynchronization processes by a prototype composing of Henon maps in a scale-free network. We show that synchronization and desynchronization of such a complex dynamical network can be determined by the network topology and the maximum Lyapunov exponent of the individual chaotic nodes.
Finite time synchronization of chaotic systems with unmatched uncertainties. In: The 30th annual conference of the IEEE industrial electronics society
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Feng Y, Sun LX, Yu XH. Finite time synchronization of chaotic systems with unmatched uncertainties. In: The 30th annual conference of the IEEE industrial electronics society, Busan, Korea; 2004.