Cluster synchronization of nonlinearly coupled Lur’e networks: Delayed impulsive adaptive control protocols

Xuan, Deli; Tang, Ze; Feng, Jianwen; Park, Ju H.

doi:10.1016/j.chaos.2021.111337

Cited by 19 publications

(10 citation statements)

References 38 publications

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“…Among these techniques, Lipchitz condition is relatively strict but a widely applied one, for example in listed papers. 12,18,26,27…”

Section: Preliminariesmentioning

confidence: 99%

“…Remark Till now, there are some linearization techniques for the nonlinear system function, such as Lipchitz condition, 12 the NCF condition, 13 the Sector condition 38 and so on. Among these techniques, Lipchitz condition is relatively strict but a widely applied one, for example in listed papers 12,18,26,27 …”

Section: Model Description and Preliminariesmentioning

confidence: 99%

“…Construct a Lur'e network with 8 delayed Lur'e systems connected in the patterns given in Figure 1. The function of an isolated Lur'e system with system delay is presented as follow 18

\kern0.5em \dot{x}(t)= Wx(t)+Z{\tilde{f}}_1\left( Ax(t)\right)+H{\tilde{f}}_2\left( Bx\left(t-{\tau}_1(t)\right)\right),

where

$$ x\kern0.5em =\left[\begin{array}{c}{x}^1(t)\\ {}{x}^2(t)\\ {}{x}^3(t)\end{array}\right],W=\left[\begin{array}{ccc}-16/3& 10& 0\\ {}1& -1& 1\\ {}0& -19.53& -0.201\end{array}\right],Z=\left[\begin{array}{c}3.247\\ {}0\\ {...

…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Over the last few decades, the synchronization issue of complex networks with diversiform time delays has been mainly investigated. For example, Xuan et al investigated the cluster synchronization of complex networks with time‐varying system delay in Reference 18. Moreover, the impulsive synchronization of complex networks with distributed coupling time delays was investigated in Reference 19.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Parameter variation‐based impulsive adaptive synchronization on Lur'e dynamical networks with hybrid time‐varying delays

Wang

Tang

Park

et al. 2023

Adaptive Control & Signal

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SummaryIn this article, the global and exponential synchronization of Lur'e networks with hybrid time‐varying delays is investigated. For sake of saving control costs, a novel impulsive adaptive controller is presented, where the adaptive feedback control input is utilized to compensate the control effects of the impulsive signal. Meanwhile, suitable control gains are obtained according to the designing on adaptive updating laws. In view of the definition of average impulsive interval, the generalized comparison principle and the formula of parameter variation, sufficient conditions for achieving global and exponential synchronization of Lur'e dynamical networks are eventually derived. Two relevant numerical simulations are provided to illustrate the effectiveness of theoretical analysis and the control scheme.

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“…Among these techniques, Lipchitz condition is relatively strict but a widely applied one, for example in listed papers. 12,18,26,27…”

Section: Preliminariesmentioning

confidence: 99%

Section: Model Description and Preliminariesmentioning

confidence: 99%

“…Construct a Lur'e network with 8 delayed Lur'e systems connected in the patterns given in Figure 1. The function of an isolated Lur'e system with system delay is presented as follow 18

\kern0.5em \dot{x}(t)= Wx(t)+Z{\tilde{f}}_1\left( Ax(t)\right)+H{\tilde{f}}_2\left( Bx\left(t-{\tau}_1(t)\right)\right),

where

$$ x\kern0.5em =\left[\begin{array}{c}{x}^1(t)\\ {}{x}^2(t)\\ {}{x}^3(t)\end{array}\right],W=\left[\begin{array}{ccc}-16/3& 10& 0\\ {}1& -1& 1\\ {}0& -19.53& -0.201\end{array}\right],Z=\left[\begin{array}{c}3.247\\ {}0\\ {...

…”

Section: Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Parameter variation‐based impulsive adaptive synchronization on Lur'e dynamical networks with hybrid time‐varying delays

Wang

Tang

Park

et al. 2023

Adaptive Control & Signal

View full text Add to dashboard Cite

show abstract

“…In light of this thought, cluster synchronization of CDNs caught much attention within the research community and admirable results have been obtained. [12][13][14] In this type of synchronization, the nodes are divided into clusters and only the nodes belonging to the same group achieve complete synchronization, whereas the nodes from different cluster groups do not synchronise. In Reference 12, a new impulsive control involving time-varying delays is designed to attain the targeted cluster synchronization for CDNs.…”

Section: Introductionmentioning

confidence: 99%

Observer‐based hybrid triggered control design for cluster synchronization of nonlinear complex dynamical networks

Devi,

Sakthivel,

Vijayakumar

et al. 2024

Adaptive Control & Signal

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SummaryThe issues of cluster synchronization and state estimation for a class of nonlinear complex dynamical networks are concurrently focused in this study. In precise, led by the design of complex dynamical networks, a proportional integral‐based observer is implemented for achieving robustness, by the virtue of which the states of examined networks are estimated. Thereupon, a proportional integral observer‐based hybrid triggered control scheme is proposed, wherein, the switch‐over between time‐ and event‐ triggered scheme is governed through a Bernoulli distributed random variable. Further, with the application of mixed and passivity performance technique, the external disturbances for the addressed complex dynamical networks are reduced. Based on the Lyapunov stability theory, the requisite sufficient conditions in respect of linear matrix inequalities are provided which ensures the discussed complex dynamical network's synchronization phenomenon. In a further, the presented criteria are exploited for the attainment of required controller, proportional and integral gain matrices. In conclusion, the applicability of proposed results and efficacy of the undertaken strategy are evidently proven with the illustration of two numerical examples with Chua's circuit and Goodwin oscillator model.

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Cluster synchronization of fractional‐order complex networks via variable‐time impulsive control

Ding,

Wang,

et al. 2024

Math Methods in App Sciences

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This paper investigates the cluster synchronization of fractional‐order complex networks. Considering that impulsive control can reduce the update of controller, and the appearance of impulse is always dependent on each node in the networks instead of appearing at fixed instant, thus we design a variable‐time impulsive controller to control the considered networks. Foremost, several assumptions are proposed to guarantee the every solution of coupled error networks intersect each discontinuous impulsive surface exactly once. In addition, by utilizing the B‐equivalence method and the theory of fractional calculus, the variable‐time impulsive fractional‐order system is reduced to a fixed‐time impulsive fractional‐order system, which can be regarded as the comparison system of the former. Next, under the framework of 1‐norm, some sufficient conditions are presented to ensure that fractional‐order system and target trajectory ultimately achieve cluster synchronization. In the end, a numerical example is designed to illustrate the validity and feasibility of theoretical results.

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Cluster synchronization of nonlinearly coupled Lur’e networks: Delayed impulsive adaptive control protocols

Cited by 19 publications

References 38 publications

Parameter variation‐based impulsive adaptive synchronization on Lur'e dynamical networks with hybrid time‐varying delays

Parameter variation‐based impulsive adaptive synchronization on Lur'e dynamical networks with hybrid time‐varying delays

Observer‐based hybrid triggered control design for cluster synchronization of nonlinear complex dynamical networks

Cluster synchronization of fractional‐order complex networks via variable‐time impulsive control

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