Synchronization in large-scale nonlinear network systems with uncertain links

• Autores: Amit Diwadkar, Umesh Vaidya
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Nº. 100, 2019, págs. 194-199
• Idioma: inglés
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• Resumen

  • In this paper, we study the problem of synchronization over a network, with nonlinear components dynamics modeled in Lure form, and linear stochastic interaction among the components. To study this problem we utilize the stochastic version of Positive Real Lemma (PRL), which is used to provide a sufficient condition for synchronization of stochastic network systems. This sufficiency condition is a function of nominal (mean coupling) Laplacian eigenvalues, and the statistics of link uncertainty in the form of coefficient of dispersion (CoD). Robust control-based small-gain interpretation is provided for the derived sufficiency condition which allows us to define the margin of synchronization. The margin of synchronization is used to understand the important tradeoff between the component dynamics, network topology, and uncertainty characteristics for network synchronization. Our results indicate that significant role played by both the largest and the second smallest eigenvalue of the nominal Laplacian in synchronization of stochastic networks. Furthermore, for a special class of network system connected over torus topology we provide an analytical expression for the tradeoff between the number of neighbors and the dimension of the torus. Similarly, by exploiting the identical nature of component dynamics computationally efficient sufficient condition, independent of network size, is provided for general class of network system. Simulation results for network of coupled oscillators with stochastic link uncertainty are presented to verify the developed theoretical framework.