On input-to-state stability for stochastic coupled control systems on networks

Gao, Shang; Wu, Boying

doi:10.1016/j.amc.2015.04.007

Cited by 10 publications

(4 citation statements)

References 44 publications

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“…On the other hand, the control problem of these nonlinear oscillator networks is also important in applications [15,38,39]. One approach of controlling the coupled oscillator network (1.1) is to apply control force f ( Ū (t) − u n i (t)) (1.4) to each oscillator for exhibiting a desired motion, e.g., u n i (t) = Ū (t) or |u n i (t) − Ū (t)| ≫ 1 for every i ∈ [n], where f (u) is a different (desirably Lipschitz continuous) function from f (u, t).…”

Section: Introductionmentioning

confidence: 99%

Continuum Limits of Coupled Oscillator Networks Depending on Multiple Sparse Graphs

Ihara,

Yagasaki

2023

J Nonlinear Sci

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The continuum limit provides a useful tool for analyzing coupled oscillator networks. Recently, Medvedev (Comm. Math. Sci., 17 (2019), no. 4, pp. 883-898) gave a mathematical foundation for such an approach when the networks are defined on single graphs which may be dense or sparse, directed or undirected, and deterministic or random. In this paper, we consider coupled oscillator networks depending on multiple graphs, and extend his results to show that the continuum limit is also valid in this situation. Specifically, we prove that the initial value problem (IVP) of the corresponding continuum limit has a unique solution under general conditions and that the solution becomes the limit of those to the IVP of the networks in some adequate meaning. Moreover, we show that if solutions to the networks are stable or asymptotically stable when the node number is sufficiently large, then so are the corresponding solutions to the continuum limit, and that if solutions to the continuum limit are asymptotically stable, then so are the corresponding solutions to the networks in some weak meaning as the node number tends to infinity. These results can also be applied to coupled oscillator networks with multiple frequencies by regarding the frequencies as a weight matrix of another graph. We illustrate the theory for three variants of the Kuramoto model along with numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Continuum Limits of Coupled Oscillator Networks Depending on Multiple Sparse Graphs

Ihara,

Yagasaki

2023

J Nonlinear Sci

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“…In recent years, coupled systems have been extensively studied for their applications in physics, ecology, epidemiology, etc. [1][2][3][4][5][6][7][8][9][10][11][12]. In particular, coupled Kuramoto oscillators (CKOs) have received a lot of attention, and their dynamical properties have been investigated by many scholars [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…So far, CKOs have been applied in various fields broadly, such as engineering, chemistry, biology and mathematics [17][18][19][20][21][22]. However, CKOs in the real world are always affected by environmental noise inevitably, which may change the dynamical properties of CKOs in general, and stochastic models are more consistent with the actual world relatively [2,[23][24][25]. In some cases, the perturbation intensity to CKOs is linear; please see the literature [23,26].…”

Section: Introductionmentioning

confidence: 99%

Stabilization for Stochastic Coupled Kuramoto Oscillators via Nonlinear Distributed Feedback Control

Kang

Gao²

2022

Mathematics

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This paper investigates the stabilization for stochastic coupled Kuramoto oscillators (SCKOs) via nonlinear distributed feedback control. An original nonlinear distributed feedback control with the advantages of fast response, no steady-state deviation, and easy implementation is designed to stabilize SCKOs. With the help of the Lyapunov method and stochastic analysis skills, some novel sufficient conditions guaranteeing the stochastic stability for SCKOs are provided by constructing a new and suitable Lyapunov function for SCKOs. Finally, a numerical example is given to illustrate the effectiveness and applicability of the theoretical result.

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“…Until now, numerous works have been done on the exponential input-tostate stability for stochastic delayed neural networks. One can see Gao and Ying [3], Lou and Ye [11], Song et al [19], Wu et al [20], Zhu and Cao [25], Zhu et al [26], Zhou et al [24] and the references therein.…”

mentioning

confidence: 99%

Weighted exponential stability of stochastic coupled systems on networks with delay driven by <inline-formula><tex-math id="M1">\begin{document}$ G $\end{document}</tex-math></inline-formula>-Brownian motion

Ren¹,

Yang²,

Yin³

2019

Discrete &Amp; Continuous Dynamical Systems - B

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This paper investigates the issue of weighted exponentially input to state stability (EISS, in short) of stochastic coupled systems on networks with time-varying delay driven by G-Brownian motion (G-SCSND, in short). Combining with inequality technique, kth vertex-Lyapunov functions and graphtheory, we establish the weighted EISS for G-SCSND. An application to the EISS for a class of stochastic coupled oscillators networks with control inputs driven by G-Brownian motion and an example are provided to illustrate the effectiveness of the obtained theory.

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On input-to-state stability for stochastic coupled control systems on networks

Cited by 10 publications

References 44 publications

Continuum Limits of Coupled Oscillator Networks Depending on Multiple Sparse Graphs

Continuum Limits of Coupled Oscillator Networks Depending on Multiple Sparse Graphs

Stabilization for Stochastic Coupled Kuramoto Oscillators via Nonlinear Distributed Feedback Control

Weighted exponential stability of stochastic coupled systems on networks with delay driven by <inline-formula><tex-math id="M1">\begin{document}$ G $\end{document}</tex-math></inline-formula>-Brownian motion

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