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Second Look at Approximating Differential Inclusions

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Author
Fahroo, Fariba
Ross, I., Michael
Date
2001-02
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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.
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Journal of Guidance, Control and Dynamics The article of record as published may be located at http://arc.aiaa.org/loi/jgcd
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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.
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http://hdl.handle.net/10945/30322
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  • Control and Optimization Laboratories
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