Exploiting Higher-order Derivatives in Computational Optimal Control
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Authors
Ross, I. Michael
Rea, Jeremy
Fahroo, Fariba
Subjects
Nonlinear systems
optimal control
discretization
higher-order derivatives
optimal control
discretization
higher-order derivatives
Advisors
Date of Issue
2002-07-09
Date
July 9-12, 2002
Publisher
American Control Conference
Language
Abstract
To facilitate generation of real-time solutions to nonlinear optimal control problems, we present a new way of approximating higher-order derivatives that arise in control systems. A Legendre pseudospectral method is presented to efficiently and accurately discretize optimal control problems governed by higher-order dynamical constraints. For mechanical systems, a reduction in the number of unknown variables is immediately realized as a consequence of Newton's second law of motion which is of second
order. The reduction in the size of the problem facilitates rapid solutions from nonlinear programming solvers. A rocket launch problem illustrates the differences in using standard state space first order forms and second-order forms. The numerical results show that the second-order form generates faster results with increasing relative computational speed for increasing grid points.
Type
Conference Paper
Description
Proceedings of the 10th Mediterranean Conference on Control and Automation -- MED 2002 , Lisbon, Portugal, July7 9-12, 2002
Series/Report No
Department
Department of Aeronautics and Astronautics
Organization
Naval Postgraduate School (U.S.)
Massachusetts Institute of Technology
Identifiers
NPS Report Number
Sponsors
Funder
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.