Optimal and Nonlinear Control Using Multiscale Methods
The idea of wavelets can be traced back to Calderon, and Coifman and Weiss. The theory was put into a rigorous framework by a number of mathematicians in the late 1980s, such as Battle, Daubechies, Mallat and others. Upto this date the use of wavelets has been focused, to a large extend, on image and signal processing applications. More recently, the advantages of wavelets for solving partial differential equations (pde's) and integral equations have been recognized. The most significant property of wavelets, compared to other basis functions, is their ability to capture the local behavior of signals both in frequency and time. Therefore, wavelet expansions can capture very accurately a signal in both domains with very few terms (i.e., wavelet coefficients). Similarly, they are inherently adaptive in the sense that one can add or remove wavelet coefficients depending on the accuracy required, without affecting the remaining coefficients. In this work we exploit the benefits of wavelets for solving optimal control problems and for on-line denoising of signals in a feedback loop.
This project is sponsored by NSF.
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