Synchronization for stochastic hybrid coupled controlled systems with Lévy noise

Zhou, Hui; Li, Yueying; Li, Wenxue

doi:10.1002/mma.6624

Cited by 23 publications

(4 citation statements)

References 38 publications

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“…In comparison to the Brownian motion, the Lévy process has been provided the possibility to describe this discontinuous process. To build more realistic models, many scholars incorporated the Lévy process into a hybrid system (Li and Deng (2017); Lu and Ding (2019); Zhou et al (2020)). Naturally, it is also very important to study the stability of hybrid systems driven by the Lévy process.…”

Section: Introductionmentioning

confidence: 99%

Stabilization and destabilization of hybrid systems by periodic stochastic controls based on Lévy noise

Fei

Liang

et al. 2023

IMA Journal of Mathematical Control and Information

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We focus in this paper on determining whether or not a periodic stochastic feedback control based on Lévy noise can stabilize or destabilize a given non-linear hybrid system. Using the Lyapunov functions and the periodic functions, we establish some sufficient conditions on the stability and instability for non-linear hybrid systems with Lévy noise. Moreover, we use some numerical examples and simulations to illustrate that an unstable (or stable) non-linear hybrid system can be stabilized (or destabilized) via periodic stochastic feedback control based on Lévy noise.

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Section: Introductionmentioning

confidence: 99%

Stabilization and destabilization of hybrid systems by periodic stochastic controls based on Lévy noise

Fei

Liang

et al. 2023

IMA Journal of Mathematical Control and Information

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“…Furthermore, in [27][28][29][30][31], the models considered have been largely restricted to deterministic ordinary differential equations. In fact, multi-weighted complex networks are inevitably affected by various types of environmental noise [33][34][35][36][37]. However, it should be noted that there are few papers about partial topology identification [32] of stochastic multi-weighted complex networks.…”

Section: Introductionmentioning

confidence: 99%

Partial Topology Identification of Stochastic Multi-Weighted Complex Networks Based on Graph-Theoretic Method and Adaptive Synchronization

Chen¹,

Zhang²,

Xu³

2023

AAMM

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This article aims to identify the partial topological structures of delayed complex network. Based on the drive-response concept, a more universal model, which includes nonlinear couplings, stochastic perturbations and multi-weights, is considered into drive-response networks. Different from previous methods, we obtain identification criteria by combining graph-theoretic method and adaptive synchronization. After that, the partial topological structures of stochastic multi-weighted complex networks with or without time delays can be identified successfully. Moreover, response network can reach synchronization with drive network. Ultimately, the effectiveness of the proposed theoretical results is validated through numerical simulations.

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“…Synchronisation, as one of the typical collective behaviours of complex dynamical networks, has stirred up great research interest over the past few decades and fruitful results have been reported (see, for example [1–10] and references therein). It is worth noting that the above literature mainly considers first‐order complex dynamical networks.…”

Section: Introductionmentioning

confidence: 99%

Synchronisation of second‐order stochastic complex dynamical networks via intermittent pinning discrete observations control and their applications

Guo

et al. 2020

IET Control Theory & Appl

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In this study, the exponential synchronisation of second‐order stochastic complex dynamical networks (SOSCDNs) is considered. A novel control called periodically intermittent pinning discrete observations control is proposed, which is based on discrete‐time state observations instead of continuous‐time state observations during the control time. To the authors' knowledge, the above control strategy has rarely been investigated in previous researches. Compared with the existing literature, there are no restrictions on the network topology structure in this study. Furthermore, by employing the Lyapunov method, stochastic analysis techniques, and matrix theory, a synchronisation criterion and a corollary about the exponential synchronisation of the SOSCDNs are presented. In particular, when the duration between two consecutive observations tends to zero, periodically intermittent pinning discrete observations control degenerates into periodically intermittent pinning control, and relevant corollaries are also derived. Finally, they applied theoretical results to single‐link robot arm systems and oscillator systems. Meanwhile, the numerical simulations are performed to demonstrate the effectiveness of their results.

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Synchronization for stochastic hybrid coupled controlled systems with Lévy noise

Cited by 23 publications

References 38 publications

Stabilization and destabilization of hybrid systems by periodic stochastic controls based on Lévy noise

Stabilization and destabilization of hybrid systems by periodic stochastic controls based on Lévy noise

Partial Topology Identification of Stochastic Multi-Weighted Complex Networks Based on Graph-Theoretic Method and Adaptive Synchronization

Synchronisation of second‐order stochastic complex dynamical networks via intermittent pinning discrete observations control and their applications

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