Publication:
Legendre pseudospectral approximations of optimal control problems

Loading...
Thumbnail Image
Authors
Ross, Michael
Fahroo, Fariba
Subjects
Advisors
Date of Issue
2003
Date
2003
Publisher
Springer
Language
Abstract
We consider nonlinear optimal control problems with mixed statecontrol constraints. A discretization of the Bolza problem by a Legendre pseudospectral method is considered. It is shown that the operations of discretization and dualization are not commutative. A set of Closure Conditions are introduced to commute these operations. An immediate consequence of this is a Covector Mapping Theorem (CMT) that provides an order-preserving transformation of the Lagrange multipliers associated with the discretized problem to the discrete covectors associated with the optimal control problem. A natural consequence of the CMT is that for pure state-constrained problems, the dual variables can be easily related to the D-form of the Lagrangian of the Hamiltonian. We demonstrate the practical advantage of our results by numerically solving a state-constrained optimal control problem without deriving the necessary conditions. The costates obtained by an application of our CMT show excellent agreement with the exact analytical solution.
Type
Article
Description
The article of record as published may be located at https://doi.org/10.1007/978-3-540-45056-6_21
Series/Report No
Department
Aeronautics and Astronautics
Identifiers
NPS Report Number
Sponsors
Funder
Format
16 p.
Citation
Ross, I. Michael, and Fariba Fahroo. "Legendre pseudospectral approximations of optimal control problems." New trends in nonlinear dynamics and control and their applications. Springer, Berlin, Heidelberg, 2003. 327-342.
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.
Collections