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Presentation
Stability Analysis of Wavelet-Controlled Dynamical Systems
Special Session on Computational and Applied Mathematics, AMS Southeastern Section Meeting, University of Richmond (2010)
  • Yan Wu, Georgia Southern University
Abstract

Compactly supported wavelets have certain properties that are useful for controller design. We explore the mechanism of a wavelet controller by integrating the wavelet controller with linear time-invariant systems (LTI). A necessary condition for an effective wavelet-based control is that the footprints of the wavelet network cover the state space where the state trajectories stay. Closed-form bounds on the design parameters of a wavelet controller are derived, which guarantee local asymptotic stability of wavelet-controlled LTI systems. Wavelet network is also effective in adaptive control of chaotic systems when there are uncertainties with the system. In this case, global stability of wavelet-control Lorenz system along with classical state feedback control is investigated. (Received August 17, 2010)

Keywords
  • Wavelets,
  • Controller design,
  • Wavelet controller,
  • Linear time-invariant systems,
  • LTI systems,
  • Lorenz system
Disciplines
Publication Date
November 6, 2010
Citation Information
Yan Wu. "Stability Analysis of Wavelet-Controlled Dynamical Systems" Special Session on Computational and Applied Mathematics, AMS Southeastern Section Meeting, University of Richmond. Richmond, VA. Nov. 2010.
source:http://www.ams.org/meetings/sectional/1065-93-46.pdf