New methods for estimation, modeling and validation of dynamical systems using automatic differentiation

摘要

The main objective of this work is to demonstrate some new computational methodsfor estimation, optimization and modeling of dynamical systems that use automaticdifferentiation. Particular focus will be upon dynamical systems arising in AerospaceEngineering. Automatic differentiation is a recursive computational algorithm, whichenables computation of analytically rigorous partial derivatives of any user-specifiedfunction. All associated computations occur, in the background without userintervention, as the name implies. The computational methods of this dissertation areenabled by a new automatic differentiation tool, OCEA (Object oriented CoordinateEmbedding Method). OCEA has been recently developed and makes possible efficientcomputation and evaluation of partial derivatives with minimal user coding. The keyresults in this dissertation details the use of OCEA through a number of computationalstudies in estimation and dynamical modeling.Several prototype problems are studied in order to evaluate judicious ways to useOCEA. Additionally, new solution methods are introduced in order to ascertain theextended capability of this new computational tool. Computational tradeoffs are studiedin detail by looking at a number of different applications in the areas of estimation,dynamical system modeling, and validation of solution accuracy for complex dynamicalsystems. The results of these computational studies provide new insights and indicatethe future potential of OCEA in its further development.