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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/3785 |
| Date | 16 August 2006 |
| Creators | Singla, Puneet |
| Contributors | Junkins, John L. |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | 24694186 bytes, electronic, application/pdf, born digital |
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