Guess-Free Trajectory Optimization
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Authors
Gong, Qi
Ross, I. Michael
Subjects
Trajectory optimization
Pontryagin's Principle
Pontryagin's Principle
Advisors
Date of Issue
2008-08-18
Date
August 18-21, 2008
Publisher
American Institute of Aeronautics and Astronautics (AIAA)
Language
Abstract
Trajectory optimization is an open-loop optimal control problem. The necessary conditions for optimal control are easy to generate by way of Pontryagin's Principle. Although these necessary conditions are powerful analysis tools, the curse of complexity has long been a major obstacle to solving the resulting boundary value problem. The Convector Mapping Principle overcomes this curse by implying that an optimal control problem is solvable if idealization is commuted with discretization. This solvability is predicated through two notions of convergence: one related to the solution and another to the algorithm. We design an elastic programming technique to exploit the divergences between these two notions of convergence while harnessing their coupling to propel a spectral algorithm. The combination of these concepts generates a globally convergent algorithm under mild conditions. In meeting the mild assumptions required of this guess-free optimization technique, the problem must be reasonably bounded and reasonably scaled. Both these requirements can be easily met for a very large family of practical problems in engineering through a new computational interpretation of the adjoins that provides useful equations for balancing the primal problem.
Type
Conference Paper
Description
The article of record as published may be located at http://dx.doi.org/10.2514/6.2008-6273
AIAA/AAS Astrodynamics Specialist Conference and Exhibit ; Paper no. AIAA-2008-6273, Honolulu, Hawaii, 2008
AIAA/AAS Astrodynamics Specialist Conference and Exhibit ; Paper no. AIAA-2008-6273, Honolulu, Hawaii, 2008
Series/Report No
Department
Organization
Optimal Guidance and Control Laboratory
Identifiers
NPS Report Number
Sponsors
Funding
NA
Format
Citation
Distribution Statement
Approved for public release; distribution is unlimited.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.