Second Look at Approximating Differential Inclusions
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Authors
Fahroo, Fariba
Ross, I., Michael
Subjects
Advisors
Date of Issue
2001-02
Date
January - February 2001
Publisher
Language
en_US
Abstract
In many direct methods for numerically solving optimal control problems, a collocation technique is used. What distinguishes numerous direct collocation schemes is the discretization of the time history and the way the state equations are satisfied at various discrete points. In one of the earliest schemes, cubic splines
were used as the interpolating polynomials over the time segments. The state differential equations were imposed at the midpoints by way of a Hermiteﾃ__Simpson implicit integration method. Generalizations
of these collocation schemes were employed by Herman and Conway and Conway and Larson in the form of higher-order Gaussﾃ__Lobatto and by Enright and Conway in the form of Rungeﾃ__Kutta-type quadrature rules. The use of higher-order integration rules facilitates a larger step size that results in a smaller number of discretization nodes or optimization variables. Because the efficiency and even convergence of nonlinear programming (NLP)problems improves for a problem of smaller size, finding ways to
accurately and ef ficiently discretize optimal control problems is of great interest in this area of research.
Type
Article
Description
Journal of Guidance, Control and Dynamics
The article of record as published may be located at http://arc.aiaa.org/loi/jgcd
Series/Report No
Department
Applied Mathematics
Identifiers
NPS Report Number
Sponsors
Naval Postgraduate School, Monterey, California.
Funder
Format
Citation
Journal of Guidance, Control, and Dynamics, Vol. 24, No. 1, January - February 2001
Distribution Statement
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.