Multi-resolution methods for high fidelity modeling and control allocation in large-scale dynamical systems

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Title: Multi-resolution methods for high fidelity modeling and control allocation in large-scale dynamical systems
Author: Singla, Puneet
Abstract: This dissertation introduces novel methods for solving highly challenging model - ing and control problems , motivated by advanced aerospace systems . Adaptable , ro - bust and computationally effcient , multi -resolution approximation algorithms based on Radial Basis Function Network and Global -Local Orthogonal Mapping approaches are developed to address various problems associated with the design of large scale dynamical systems . The main feature of the Radial Basis Function Network approach is the unique direction dependent scaling and rotation of the radial basis function via a novel Directed Connectivity Graph approach . The learning of shaping and rota - tion parameters for the Radial Basis Functions led to a broadly useful approximation approach that leads to global approximations capable of good local approximation for many moderate dimensioned applications . However , even with these refinements , many applications with many high frequency local input /output variations and a high dimensional input space remain a challenge and motivate us to investigate an entirely new approach . The Global -Local Orthogonal Mapping method is based upon a novel averaging process that allows construction of a piecewise continuous global family of local least -squares approximations , while retaining the freedom to vary in a general way the resolution (e .g . , degrees of freedom ) of the local approximations . These approximation methodologies are compatible with a wide variety of disciplines such as continuous function approximation , dynamic system modeling , nonlinear sig -nal processing and time series prediction . Further , related methods are developed for the modeling of dynamical systems nominally described by nonlinear differential equations and to solve for static and dynamic response of Distributed Parameter Sys - tems in an effcient manner . Finally , a hierarchical control allocation algorithm is presented to solve the control allocation problem for highly over -actuated systems that might arise with the development of embedded systems . The control allocation algorithm makes use of the concept of distribution functions to keep in check the "curse of dimensionality" . The studies in the dissertation focus on demonstrating , through analysis , simulation , and design , the applicability and feasibility of these ap - proximation algorithms to a variety of examples . The results from these studies are of direct utility in addressing the "curse of dimensionality" and frequent redundancy of neural network approximation .
URI: http : / /hdl .handle .net /1969 .1 /3785
Date: 2006-08-16

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Multi-resolution methods for high fidelity modeling and control allocation in large-scale dynamical systems. Available electronically from http : / /hdl .handle .net /1969 .1 /3785 .

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