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Stability Analysis of Wavelet-Controlled Dynamical Systems
Fall Southeastern Sectional Meeting of the American Mathematical Society (AMS) (2010)
  • Yan Wu, Georgia Southern University
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.
  • Wavelets,
  • Controller design,
  • Wavelet controller,
  • Linear time-invariant systems,
  • LTI systems,
  • Lorenz system
Publication Date
November 6, 2010
Richmond, VA
Citation Information
Yan Wu. "Stability Analysis of Wavelet-Controlled Dynamical Systems" Fall Southeastern Sectional Meeting of the American Mathematical Society (AMS) (2010)
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