Neural Modelling with Wavelets and Application in Adaptive/Learning Control

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dc.contributor.advisorKrishnaprasad, P.S.en_US
dc.contributor.authorKugarajah, Tharmarajahen_US
dc.contributor.departmentISRen_US
dc.date.accessioned2007-05-23T10:00:27Z
dc.date.available2007-05-23T10:00:27Z
dc.date.issued1995en_US
dc.description.abstractSpatio-spectral properties of the Wavelet Transform provide a useful theoretical framework to investigate the structure of neural networks. A few researchers (Pati & Krishnaprasad, Zhang & Benveniste) have investigated the connection between neural networks and wavelet transforms. However, a number of issues remain unresolved especially when the connection is considered in the multidimensional case. In our work, we resolve these issues by extensions based on some theorems of Daubechies related to wavelet frames and provide a frame-work to analyze local learning in neural-networks.<P>We also provide a constructive procedure to build networks based on wavelet theory. Moreover, cognizant of the problems usually encountered in practical implementations of these ideas, we develop a heuristic methodology, inspired by similar work in the area of Radial Basis Function (RBF) networks (Moody & Darken, Platt), to build a network sequentially on-line as well as off-line.<P>We show some connections of our method to some existing methods such as Projection Pursuit Regression (Friedman), Hyper Basis Functions (Poggio & Girosi) and other methods that have been proposed in the literature on neural- networks as well as statistics. In particular, some classes of wavelets can also be derived from the regularization theoretical framework given by Poggio & Girosi.<P>Finally, we choose direct nonlinear adaptive control to demonstrate the utility of the network in the context of local learning. Stability analysis is carried out within a standard Lyapunov formulation. Simulation studies show the effectiveness of these methods. We compare and contrast these methods with some recent results obtained by other researchers using Back Propagation (Feed-Forward) Networks, and Gaussian Networks.en_US
dc.format.extent2190555 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1903/5701
dc.language.isoen_USen_US
dc.relation.ispartofseriesISR; MS 1995-1en_US
dc.subjectneural systemsen_US
dc.subjectadaptive controlen_US
dc.subjectnonlinear systemsen_US
dc.subjectwaveletsen_US
dc.subjectbasic functionen_US
dc.subjectintelligent servoen_US
dc.subjectIntelligent Control Systemsen_US
dc.titleNeural Modelling with Wavelets and Application in Adaptive/Learning Controlen_US
dc.typeThesisen_US

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