scholarly journals Robust Group Synchronization via Cycle-Edge Message Passing

2021 ◽  
Author(s):  
Gilad Lerman ◽  
Yunpeng Shi
Keyword(s):  
Gaussian Noise ◽  
Message Passing ◽  
General Framework ◽  
Linear Convergence ◽  
Small Noise ◽  
Synchronization Problem ◽  
Group Synchronization ◽  
The Stability ◽  
Synchronization Problems ◽  
Deterministic Setting

AbstractWe propose a general framework for solving the group synchronization problem, where we focus on the setting of adversarial or uniform corruption and sufficiently small noise. Specifically, we apply a novel message passing procedure that uses cycle consistency information in order to estimate the corruption levels of group ratios and consequently solve the synchronization problem in our setting. We first explain why the group cycle consistency information is essential for effectively solving group synchronization problems. We then establish exact recovery and linear convergence guarantees for the proposed message passing procedure under a deterministic setting with adversarial corruption. These guarantees hold as long as the ratio of corrupted cycles per edge is bounded by a reasonable constant. We also establish the stability of the proposed procedure to sub-Gaussian noise. We further establish exact recovery with high probability under a common uniform corruption model.

Solving Vlasov-Poisson-Fokker-Planck Equations using NRxx method

2017 ◽  
Vol 21 (3) ◽  
pp. 782-807 ◽  
Author(s):  
Yanli Wang ◽  
Shudao Zhang
Keyword(s):  
Splitting Method ◽  
Linear Convergence ◽  
Mass Conservation ◽  
System A ◽  
Spectral Convergence ◽  
The Stability ◽  
The Moment ◽  
Stability And Accuracy ◽  
Fokker Planck Equations ◽  
Fokker Planck

AbstractWe present a numerical method to solve the Vlasov-Poisson-Fokker-Planck (VPFP) system using the NRxx method proposed in [4, 7, 9]. A globally hyperbolic moment system similar to that in [23] is derived. In this system, the Fokker-Planck (FP) operator term is reduced into the linear combination of the moment coefficients, which can be solved analytically under proper truncation. The non-splitting method, which can keep mass conservation and the balance law of the total momentum, is used to solve the whole system. A numerical problem for the VPFP system with an analytic solution is presented to indicate the spectral convergence with the moment number and the linear convergence with the grid size. Two more numerical experiments are tested to demonstrate the stability and accuracy of the NRxx method when applied to the VPFP system.

Cyclic Constraint Analysis for Attitude Synchronization of Networked Spacecraft Agents

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Hanlei Wang ◽  
Yongchun Xie
Keyword(s):  
Multiple Equilibria ◽  
Closed Loop ◽  
Euler Parameters ◽  
Networked System ◽  
Synchronization Errors ◽  
Synchronization Problem ◽  
Constraint Analysis ◽  
The Stability ◽  
Error Orientation ◽  
Attitude Synchronization

In this paper, we investigate the attitude synchronization problem for multiple networked spacecraft, and the spacecraft agents are assumed to interact on an undirected and connected graph. We adopt a physically motivated PD-like attitude consensus scheme which takes Euler parameters or quaternions of the error orientation matrix between the spacecraft agents as the attitude deviation, resulting in nonlinear attitude coupling among the networked spacecraft agents and additionally multiple equilibria of the closed-loop networked system. The stability of the closed-loop networked system is shown by the Lyapunov stability analysis. To show the convergence of the attitude synchronization errors, we develop a new tool called cyclic constraint analysis. With this synthesis tool, we show that attitude synchronization is achieved without relying on any assumptions of the spacecraft orientations. Simulation study is presented to shed some light on the obtained results.

scholarly journals Pinning Synchronization of Nonlinearly Coupled Complex Dynamical Networks on Time Scales

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Fang-Di Kong
Keyword(s):  
Time Scales ◽  
Discrete Time ◽  
Control Strategy ◽  
Continuous Time ◽  
General Framework ◽  
Pinning Control ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Numerical Examples ◽  
Synchronization Problem

In this paper, we study the synchronization problem for nonlinearly coupled complex dynamical networks on time scales. To achieve synchronization for nonlinearly coupled complex dynamical networks on time scales, a pinning control strategy is designed. Some pinning synchronization criteria are established for nonlinearly coupled complex dynamical networks on time scales, which guarantee the whole network can be pinned to some desired state. The model investigated in this paper generalizes the continuous-time and discrete-time nonlinearly coupled complex dynamical networks to a unique and general framework. Moreover, two numerical examples are given for illustration and verification of the obtained results.

SYNCHRONIZATION OF UNCERTAIN CHAOTIC SYSTEMS BASED ON THE FUZZY-MODEL-BASED APPROACH

2006 ◽  
Vol 16 (05) ◽  
pp. 1435-1444 ◽  
Author(s):  
H. K. LAM ◽  
F. H. F. LEUNG
Keyword(s):  
Chaotic Systems ◽  
Fuzzy Model ◽  
Parameter Design ◽  
Parameter Uncertainties ◽  
Model Based ◽  
Synchronization Problem ◽  
Programming Techniques ◽  
Uncertain Chaotic Systems ◽  
Switching Controller ◽  
The Stability

This paper investigates the synchronization of chaotic systems subject to parameter uncertainties. Based on the fuzzy-model-based approach, a switching controller will be proposed to deal with the synchronization problem. The stability conditions will be derived based on the Lyapunov approach. The tracking performance and parameter design of the proposed switching controller will be formulated as a generalized eigenvalue minimization problem which can be solved numerically using some convex programming techniques. Simulation examples will be given to show the effectiveness of the proposed approach.

scholarly journals Synchronization of Two Non-Identical Coupled Exciters in a Non-Resonant Vibrating System of Linear Motion. Part I: Theoretical Analysis

2009 ◽  
Vol 16 (5) ◽  
pp. 505-515 ◽  
Author(s):  
Chunyu Zhao ◽  
Hongtao Zhu ◽  
Ruizi Wang ◽  
Bangchun Wen
Keyword(s):  
Zero Solution ◽  
Moment Of Inertia ◽  
Moments Of Inertia ◽  
Vibrating System ◽  
Frequency Capture ◽  
Synchronization Problem ◽  
Small Parameters ◽  
Existence And Stability ◽  
Synchronous Operation ◽  
The Stability

In this paper an analytical approach is proposed to study the feature of frequency capture of two non-identical coupled exciters in a non-resonant vibrating system. The electromagnetic torque of an induction motor in the quasi-steady-state operation is derived. With the introduction of two perturbation small parameters to average angular velocity of two exciters and their phase difference, we deduce the Equation of Frequency Capture by averaging two motion equations of two exciters over their average period. It converts the synchronization problem of two exciters into that of existence and stability of zero solution for the Equation of Frequency Capture. The conditions of implementing frequency capture and that of stabilizing synchronous operation of two motors have been derived. The concept of torque of frequency capture is proposed to physically explain the peculiarity of self-synchronization of the two exciters. An interesting conclusion is reached that the moments of inertia of the two exciters in the Equation of Frequency Capture reduce and there is a coupling moment of inertia between the two exciters. The reduction of moments of inertia and the coupling moment of inertia have an effect on the stability of synchronous operation.

Adaptive Neuro-Fuzzy Synchronization in Isolated Power Systems with High Wind Penetration

2016 ◽  
Vol 20 (3) ◽  
pp. 418-428
Author(s):  
Michael Negnevitsky ◽  
◽  
Dusan Nikolic ◽  
Martin de Groot ◽  
◽  
...  
Keyword(s):  
Power Systems ◽  
Diesel Generator ◽  
Synchronization Problem ◽  
Neuro Fuzzy ◽  
Harmful Emissions ◽  
Diesel Generators ◽  
The Stability ◽  
Systems Simulation ◽  
System Frequency

Isolated power systems (IPSs) worldwide are traditionally powered by diesel generators that are very expensive to run and produce harmful emissions. In order to mitigate these problems, wind turbines are being introduced into existing IPSs. Although this integration has been reasonably effective at reducing running costs and emissions, high levels of wind penetration cause large system frequency variations, resulting in a prolonged synchronization process for newly dispatched diesel generators. Long synchronization can compromise the stability of a small IPS. This paper examines the diesel synchronization problem using a real IPS as a case study and offers a solution by introducing the concept of predictive synchronization based on adaptive neuro-fuzzy systems. Simulation results demonstrate a significant reduction in diesel generator synchronization times.

scholarly journals How to synchronize an out of sync system?

2021 ◽  
Author(s):  
Kahina Louadj ◽  
Philippe Marthon
Keyword(s):  
Optimal Solution ◽  
Optimization Criterion ◽  
Tracking Algorithm ◽  
Initial State ◽  
Synchronization Problem ◽  
Robot Systems ◽  
Asymptotic Synchronization ◽  
Synchronization Problems ◽  
General Method ◽  
Do So

Synchronization with other machines is one of those tasks that an intelligent machine should be able to perform. To do so, a general method of synchronization must be defined and that is the ambition of this article. For this purpose, we recall what the main concepts of systemic modelling consist of. Then we define what a Synchronization Problem is and distinguish three types of synchronization problems : predetermined (PSP), stochastic (SSP) and asymptotic (ASP). So, to find the best solution, we define three optimized synchronization problems : Optimized Predetermined Synchronization Problems , Optimized Stochastic Synchronization Problems (OSSP) and Optimized Asymptotic Synchronization Problems (OASP). A general method for solving an optimized synchronization problem and thus synchronize an out of sync system, is then given; it includes four steps : step 1, identify the synchronization functions; step 2, identify the synchronization case : predetermined, stochastic or asymptotic; step 3, select an optimization criterion and solve the optimized synchronization problem corresponding to the chosen synchronization case; step 4, find a control which permits to track the system trajectory, optimal solution of the selected optimized synchronization problem. In the next section, we present a heuristic algorithm that checks the constraints of an ASP for any initial state of the system to be synchronized. The principle of this algorithm is to pursue or track a perfectly synchronized solution. Finally, we present and solve two synchronization problems in the field of Mobile Robot Systems: a synchronized satelliteization problem and the Horse Carousel Problem. We apply to these two problems the general method given above by choosing the asymptotic synchronization case and our tracking algorithm. Simulation results show the efficiency of the method and the relevance of using a tracking algorithm.

scholarly journals Synchronization of the Glycolysis Reaction-Diffusion Model via Linear Control Law

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1516
Author(s):  
Adel Ouannas ◽  
Iqbal M. Batiha ◽  
Stelios Bekiros ◽  
Jinping Liu ◽  
Hadi Jahanshahi ◽  
...  
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Linear Control ◽  
Control Law ◽  
Synchronization Problem ◽  
Reaction Diffusion Model ◽  
Spatial Dimensions ◽  
Error System ◽  
The Stability ◽  
Complex Formations

The Selkov system, which is typically employed to model glycolysis phenomena, unveils some rich dynamics and some other complex formations in biochemical reactions. In the present work, the synchronization problem of the glycolysis reaction-diffusion model is handled and examined. In addition, a novel convenient control law is designed in a linear form and, on the other hand, the stability of the associated error system is demonstrated through utilizing a suitable Lyapunov function. To illustrate the applicability of the proposed schemes, several numerical simulations are performed in one- and two-spatial dimensions.

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