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Numerical Derivative Techniques for Trajectory OptimizationThe adoption of robust numerical optimization techniques in trajectory simulation programs has resulted in powerful design and analysis tools. These trajectory simulation/optimization programs are widely used, and a representative list includes the GTS system, the POST program, and newer collocation methods such as OTIS and FONPAC. All of these programs rely on optimization algorithms which require objective function and constraint gradient data during the iteration process. However, most trajectory optimization problems lack simple analytical expressions for these derivatives. In the general case a function evaluation involves integrating aerodynamic, propulsive, and gravity forces over multiple trajectory phases with complex control models. With the newer collocation methods, the integration is replaced by defect constraints and cubic approximations for the state. While analytic gradient expressions can sometimes be derived for trajectory optimization problems, the derivation is cumbersome, time consuming, and prone to mistakes. Fortunately, an alternate method exists for the gradient evaluation, namely finite difference approximations. In this paper some finite difference gradient techniques developed for use with the GTS system are presented. These techniques include methods for computing first and second partial derivatives of single and multiple sets of functions. A key feature of these methods is an error control mechanism which automatically adjusts the perturbation size to obtain accurate derivative values.
Document ID
19940004719
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Wayne P Hallman
(Aerospace Corp. El Segundo, CA, United States)
Date Acquired
August 16, 2013
Publication Date
September 24, 1990
Publication Information
Publication: The Third Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization
Publisher: National Aeronautics and Space Administration
Subject Category
Computer Programming And Software
Meeting Information
Meeting: 3rd Symposium on Recent Advances in Multidisciplinary Analysis and Optimization
Location: San Francisco, CA
Country: US
Start Date: September 24, 1990
End Date: September 26, 1990
Sponsors: United States Department of the Air Force, National Aeronautics and Space Administration
Accession Number
94N71474
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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