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Description:
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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 . |