Costate Estimation by a Legendre Pseudospectral Method
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Authors
Fahroo, Fariba
Ross, I. Michael
Subjects
Optimal control
Advisors
Date of Issue
2001-03-01
Date
March-April 2001
Publisher
Naval Postgraduate School (U.S.)
Language
Abstract
We present a Legendre pseudospectral method for directly estimating the costate of the Bolza problem encountered in optimal control theory. The method is based on calculating the state and control variables at the Legendre'Gauss'Lobatto (LGL) points. An Nth degree Lagrange polynomial approximation of these variables allows a conversion of the optimal control problem into a standard nonlinear programming (NLP) problem with the state and control values at the LGL points as optimization parameters. By applying the Karush'Kuhn'Tucker (KKT) theorem to the NLP problem, we show that the KKT multipliers satisfy a discrete analog of the costate
dynamics including the transversality conditions. Indeed, we prove that the costates at the LGL points are equal to the KKT multipliers divided by the LGL weights. Hence, the direct solution by this method also automatically yields the costate by way of the Lagrange multipliers that can be extracted from an NLP solver. One important
advantage of this technique is that it allows a very simple way to check the optimality of the direct solution. Numerical examples are included to demonstrate the method.
Type
Conference Paper
Description
Journal of Guidance, Control, and Dynamics Vol. 24, No. 2, March-April 2001
Series/Report No
Department
Department of Aeronautics and Astronautics
Mathematics
Organization
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.