Global Frequency Synchronization over Networks of Uncertain Second-Order Kuramoto Oscillators via Distributed Adaptive Tracking

2019 ◽  
Author(s):  
Alessandro Bosso ◽  
Ilario A. Azzollini ◽  
Simone Baldi
Keyword(s):  
Second Order ◽  
Frequency Synchronization ◽  
Adaptive Tracking ◽  
Kuramoto Oscillators

Remarks on the complete synchronization for the Kuramoto model with frustrations

2018 ◽  
Vol 16 (04) ◽  
pp. 525-563 ◽  
Author(s):  
Seung-Yeal Ha ◽  
Hwa Kil Kim ◽  
Jinyeong Park
Keyword(s):  
Phase Synchronization ◽  
Kuramoto Model ◽  
Prototype Model ◽  
Frequency Synchronization ◽  
Complete Synchronization ◽  
Synchronization Problem ◽  
Kuramoto Oscillators ◽  
Applicable Range ◽  
The Kuramoto Model ◽  
Complete Frequency

The synchronous dynamics of many limit-cycle oscillators can be described by phase models. The Kuramoto model serves as a prototype model for phase synchronization and has been extensively studied in the last 40 years. In this paper, we deal with the complete synchronization problem of the Kuramoto model with frustrations on a complete graph. We study the robustness of complete synchronization with respect to the network structure and the interaction frustrations, and provide sufficient frameworks leading to the complete synchronization, in which all frequency differences of oscillators tend to zero asymptotically. For a uniform frustration and unit capacity, we extend the applicable range of initial configurations for the complete synchronization to be distributed on larger arcs than a half circle by analyzing the detailed dynamics of the order parameters. This improves the earlier results [S.-Y. Ha, H. Kim and J. Park, Remarks on the complete frequency synchronization of Kuramoto oscillators, Nonlinearity 28 (2015) 1441–1462; Z. Li and S.-Y. Ha, Uniqueness and well-ordering of emergent phase-locked states for the Kuramoto model with frustration and inertia, Math. Models Methods Appl. Sci. 26 (2016) 357–382.] which can be applicable only for initial configurations confined in a half circle.

scholarly journals Condensation of Synchronous Orbits on Complex Networks

2021 ◽  
Author(s):  
Ruiwu Niu ◽  
Xiaoqun Wu ◽  
Jianwen Feng ◽  
Gui-jun Pan ◽  
Jun-an Lu ◽  
...  
Keyword(s):  
Statistical Mechanics ◽  
Complex Networks ◽  
Numerical Simulations ◽  
Phase Synchronization ◽  
Single Layer ◽  
The Other ◽  
Frequency Synchronization ◽  
Synchronization Process ◽  
Mechanics Analysis ◽  
Kuramoto Oscillators

Abstract In this paper we study frequency synchronization of Kuramoto oscillators. We find a typical phenomenon of condensed synchronous orbits on single-layer or duplex networks through statistical mechanics analysis and numerical simulations, where the distribution of synchronous orbits is in a bell-shaped form. Further, we investigate phase synchronization on single-layer and duplex networks with different distributions of inherent frequencies. We find that normally distributed inherent frequencies with low variances are more beneficial for phase synchronization, and separately distributed inherent frequencies can slow down the synchronization process. In the end, we investigate the influence of one layer's inherent frequencies on the other layer's phase synchronization through inter-layer couplings. Interestingly, we find that one layer's inherent frequencies with a highly condensed distribution can greatly improve phase synchronization on the other layer. The results shed new lights to our understanding of the nature of synchronization on single-layer as well as multilayer complex networks of coupled Kuramoto oscillators.

scholarly journals Adaptive Tracking Control for the Piezoelectric Actuated Stage Using the Krasnosel’skii-Pokrovskii Operator

Micromachines ◽  
2020 ◽  
Vol 11 (5) ◽  
pp. 537 ◽  
Author(s):  
Rui Xu ◽  
Dapeng Tian ◽  
Zhongshi Wang
Keyword(s):  
Linear Equation ◽  
Tracking Control ◽  
Control Method ◽  
Second Order ◽  
Unknown Parameters ◽  
Order Linear ◽  
Adaptive Tracking Control ◽  
Adaptive Tracking ◽  
Hysteresis Nonlinearity ◽  
Gradient Descent Algorithm

In this paper, a discrete second order linear equation with the Krasnosel’skii-Pokrovskii (KP) operator is used to describe the piezoelectric actuated stage. The weights of the KP operators are identified by the gradient descent algorithm. To suppress the hysteresis nonlinearity of the piezoelectric actuated stage, this paper proposes an adaptive tracking control with the hysteresis decomposition on the designed error surface. The proposed adaptive tracking controller dispenses with any form of the feed-forward hysteresis compensation and the unknown parameters of the discrete second order linear equation are adaptively adjusted. Some simulations are implemented to verify the effectiveness of the KP operators, then a series of modeling and control experiments are carried out on the piezoelectric actuated stages experimental systems. The comparative experimental results verify the feasibility of the KP operators modeling method and the adaptive tracking control method.

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