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Description:
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The main objective of this work is to demonstrate some new computational methods
for estimation , optimization and modeling of dynamical systems that use automatic
differentiation . Particular focus will be upon dynamical systems arising in Aerospace
Engineering . Automatic differentiation is a recursive computational algorithm , which
enables computation of analytically rigorous partial derivatives of any user -specified
function . All associated computations occur , in the background without user
intervention , as the name implies . The computational methods of this dissertation are
enabled by a new automatic differentiation tool , OCEA (Object oriented Coordinate
Embedding Method ) . OCEA has been recently developed and makes possible efficient
computation and evaluation of partial derivatives with minimal user coding . The key
results in this dissertation details the use of OCEA through a number of computational
studies in estimation and dynamical modeling .
Several prototype problems are studied in order to evaluate judicious ways to use
OCEA . Additionally , new solution methods are introduced in order to ascertain the
extended capability of this new computational tool . Computational tradeoffs are studied
in detail by looking at a number of different applications in the areas of estimation ,
dynamical system modeling , and validation of solution accuracy for complex dynamical
systems . The results of these computational studies provide new insights and indicate
the future potential of OCEA in its further development . |