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Content Provider | IEEE Xplore Digital Library |
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Author | Qing Hui |
Copyright Year | 2011 |
Description | Author affiliation: Department of Mechanical Engineering, Texas Tech University, Lubbock, 79409-1021, USA (Qing Hui) |
Abstract | This paper addresses the convergence and stability analysis for iterative processes such as numerical iterative algorithms by using a novel trajectory distance based approach. Iterative dynamics are widespread in distributed algorithms and numerical analysis. However, efficient analysis of convergence and sensitivity of iterative dynamics is quite challenging due to the lack of systematic tools. For instance, the trajectories of iterative dynamics are usually not continuous with respect to the initial condition. Hence, the classical dynamical systems theory cannot be applied directly. In this paper, a trajectory distance based Lyapunov approach is proposed as a means to tackling convergence and sensitivity to the initial condition of iterative processes. Technically the problem of convergence and sensitivity is converted into finiteness of trajectory distance and semistability analysis of discrete-time systems. A semidefinite Lyapunov function based trajectory distance approach is proposed to characterize convergence and semistability of iterative dynamics. Two examples are provided to elucidate the proposed method. Finally, the proposed framework is used to solve the convergence and stability of iterative algorithms developed for balanced resource allocation and damage mitigation problems under adversarial attacks. |
Starting Page | 7218 |
Ending Page | 7223 |
File Size | 181434 |
Page Count | 6 |
File Format | |
ISBN | 9781612848006 |
ISSN | 07431546 |
e-ISBN | 9781612848013 |
e-ISBN | 9781612847993 |
DOI | 10.1109/CDC.2011.6160322 |
Language | English |
Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
Publisher Date | 2011-12-12 |
Publisher Place | USA |
Access Restriction | Subscribed |
Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
Subject Keyword | Convergence Trajectory Peer to peer computing Iterative methods Sensors Mobile communication Stability analysis |
Content Type | Text |
Resource Type | Article |
Subject | Control and Optimization Control and Systems Engineering Modeling and Simulation |
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