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.
| Original language | American English |
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| State | Published - Nov 6 2010 |
| Event | Fall Southeastern Sectional Meeting of the American Mathematical Society (AMS) - Richmond, VA Duration: Nov 6 2010 → … |
Conference
| Conference | Fall Southeastern Sectional Meeting of the American Mathematical Society (AMS) |
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| Period | 11/6/10 → … |
Keywords
- Controller design
- LTI systems
- Linear time-invariant systems
- Lorenz system
- Wavelet controller
- Wavelets
DC Disciplines
- Mathematics