Synchronization in a fractional-order dynamic network with uncertain parameters using an adaptive control strategy

Du, Lin; Lei, Youming; Yang, Yong

doi:10.1007/s10483-018-2304-9

Cited by 13 publications

(9 citation statements)

References 26 publications

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“…That is, the fractional dynamical networks can more precisely describe the characteristics of physical systems. Nowadays, many valuable results about the fractional-order networks have been obtained [18][19][20][21][22][23][24][25]. In [18], Si et al gave the sufficient condition of structure identification in uncertain fractional dynamical networks, and further discussed the effects of coupling strength and fractional order on the identification process.…”

Section: Introductionmentioning

confidence: 99%

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Structure Identification of Fractional-Order Dynamical Network with Different Orders

Zhou

2021

Mathematics

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Topology structure and system parameters have a great influence on the dynamical behavior of dynamical networks. However, they are sometimes unknown or uncertain in advance. How to effectively identify them has been investigated in various network models, from integer-order networks to fractional-order networks with the same order. In the real world, many systems consist of subsystems with different fractional orders. Therefore, the structure identification of a dynamical network with different fractional orders is investigated in this paper. Through designing proper adaptive controllers and parameter updating laws, two network estimators are well constructed. One is for identifying only the unknown topology structure. The other is for identifying both the unknown topology structure and system parameters. Based on the Lyapunov function method and the stability theory of fractional-order dynamical systems, the theoretical results are analytically proved. The effectiveness is verified by three numerical examples as well. In addition, the designed estimators have a good performance in monitoring switching topology. From the practical viewpoint, the designed estimators can be used to monitor the change of current and voltage in the fractional-order circuit systems.

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Section: Introductionmentioning

confidence: 99%

“…It is worth noting that the networks in the aforementioned literature [18][19][20][21][22][23][24][25][26][27][28] are formed by many coupled subsystems with the same fractional order. In fact, complex networks may consist of subsystems with different fractional orders in the real world.…”

Section: Introductionmentioning

confidence: 99%

Structure Identification of Fractional-Order Dynamical Network with Different Orders

Zhou

2021

Mathematics

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“…It is easy to understand that the key to dynamic control is to achieve high-efficiency synchronization between given complex networks [21][22][23][24] . Depending on the dynamics features of studied systems, researchers have proposed many control methods to obtain synchronization, e.g., adaptive synchronization, pinning synchronization, sliding mode synchronization [25][26][27][28] .…”

Section: Introductionmentioning

confidence: 99%

Sliding mode synchronization between uncertain Watts-Strogatz small-world spatiotemporal networks

Liu

Wang

2020

Appl. Math. Mech.-Engl. Ed.

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Based on the topological characteristics of small-world networks, a nonlinear sliding mode controller is designed to minimize the effects of internal parameter uncertainties. To qualify the effects of uncertain parameters in the response networks, some effective recognition rates are designed so as to achieve a steady value in the extremely fast simulation time period. Meanwhile, the Fisher-Kolmogorov and Burgers spatiotemporal chaotic systems are selected as the network nodes for constructing a drive and a response network, respectively. The simulation results confirm that the developed sliding mode could realize the effective synchronization problem between the spatiotemporal networks, and the outer synchronization is still achieved timely even when the connection probability of the small-world networks changes.

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“…In order to achieve network synchronization, some advisable methods are introduced in outstanding works (e.g., [17][18][19][20][21][22][23][24][25][26][27][28]), such as pinning control [17][18][19] and adaptive strategies [20][21][22][23][24][25][26][27][28]. In [25], the authors introduced the adaptive coupling strengths and studied the adaptive synchronization of two heterogeneous second-order nonlinear coupled dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

“…e synchronization of fractional-order complex networks were well considered in [26][27][28] and applying decentralized adaptive strategies, pinning control and adaptive control strategy, respectively.…”

Section: Introductionmentioning

confidence: 99%

Sampled-Data-Based Adaptive Group Synchronization of Second-Order Nonlinear Complex Dynamical Networks with Time-Varying Delays

Liu

Bai

Zhao

et al. 2020

Mathematical Problems in Engineering

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This paper studies the adaptive group synchronization of second-order nonlinear complex dynamical networks with sampled-data and time-varying delays by designing a new adaptive strategy to feedback gains and coupling strengths. According to Lyapunov stability properties, it is shown that the agents of subgroups can converge the given synchronous states, respectively, under some conditions on the sampled period. Moreover, some simulation results are given.

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Synchronization in a fractional-order dynamic network with uncertain parameters using an adaptive control strategy

Cited by 13 publications

References 26 publications

Structure Identification of Fractional-Order Dynamical Network with Different Orders

Structure Identification of Fractional-Order Dynamical Network with Different Orders

Sliding mode synchronization between uncertain Watts-Strogatz small-world spatiotemporal networks

Sampled-Data-Based Adaptive Group Synchronization of Second-Order Nonlinear Complex Dynamical Networks with Time-Varying Delays

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