A sliding mode approach to H∞ synchronization of master–slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties

Abstract-In this paper, the distributed synchronization problem of networks of agent systems with controllers and nonlinearities subject to Bernoulli switchings is investigated. Controllers and adaptive updating laws injected in each vertex of networks depend on the state information of its neighborhood. Three sets of Bernoulli stochastic variables are introduced to describe the occurrence probabilities of distributed adaptive controllers, updating laws and nonlinearities, respectively. By the Lyapunov functions method, we show that the distributed synchronization of networks composed of agent systems with multiple randomly occurring nonlinearities, multiple randomly occurring controllers, and multiple randomly occurring updating laws can be achieved in mean square under certain criteria. The conditions derived in this paper can be solved by semi-definite programming. Moreover, by mathematical analysis, we find that the coupling strength, the probabilities of the Bernoulli stochastic variables, and the form of nonlinearities have great impacts on the convergence speed and the terminal control strength. The synchronization criteria and the observed phenomena are demonstrated by several numerical simulation examples. In addition, the advantage of distributed adaptive controllers over conventional adaptive controllers is illustrated.Index Terms-Bernoulli stochastic variables, complex dynamical networks, distributed synchronization, multi-agent systems, multiple random nonlinearities, multiple random updating laws.

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“…Event 3 : (6) experiences (8) Event 4 : (6) does not experience (8). (9) Here, ξ i (t) is defined by…”

Section: Remarkmentioning

confidence: 99%

“…The problem of such models was widely studied in the literature, see [4] and references therein. Also, the control and updating failure in the considered system can also be modeled by Markovian switching [8] and switching signals [39], which would be more general than our model.…”

Section: Remarkmentioning

confidence: 99%

Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings

Tang

Gao

Zou

et al. 2013

IEEE Trans. Cybern.

270

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“…To solve this problem, the sliding mode control (SMC) provides a good solution. Up to now, many relevant researches have been carried out [1][2][3][4][5][6][7][8][9][10][11][12][13] . Based on SMC, the authors in [2] investigated the robust adaptive control problem for fuzzy systems with mismatched uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy sliding mode control design for a class of disturbed systems

Wang

Shi

Karimi

2014

Journal of the Franklin Institute

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This paper discusses the problem of the fuzzy sliding mode control for a class of disturbed systems. First, a fuzzy auxiliary controller is constructed based on a feedback signal not only to estimate the unknown control term, but also participates in the sliding mode control due to the fuzzy rule employed. Then, we extend our theory into the cases, where some kind of system information can not be obtained, for better use of our theoretical results in real engineering. Finally, some typical numerical examples are included to demonstrate the effectiveness and advantage of the designed sliding mode controller. © 2013 The Franklin Institute

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“…In In Sun (2009), via the time-domain approach, a tracking control is proposed to realize chaos synchronization for the uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity. In Wu et al (2009) Recently, the problem of synchronization for dierent class of master-slave systems with time-delays and uncertainties are studied in (Karimi and Gao (2010), Karimi et al (2012), Karimi (2012), Karimi (2011)) and the references therein. However, those synchronization methods usually are specialized for one typical chaotic system, which limit their application in practice.…”

Section: Introductionmentioning

confidence: 99%

-Infinity robust controller design for the synchronization of master-slave chaotic systems with disturbance input

Wang¹,

Shi²,

Karimi³

et al. 2012

MIC

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This paper is concerned with the robust control problems for the synchronization of master-slave chaotic systems with disturbance input. By constructing a series of Lyapunov functions, novel H ∞ robust synchronization controllers are designed, whose control regulation possess the characteristic of simpleness and explicitness. Finally, numerical simulations are provided to demonstrate the eectiveness of the proposed techniques.

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A sliding mode approach to H∞ synchronization of master–slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties

Cited by 271 publications

References 47 publications

Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings

Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings

Fuzzy sliding mode control design for a class of disturbed systems

-Infinity robust controller design for the synchronization of master-slave chaotic systems with disturbance input

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