Legendre pseudospectral approximations of optimal control problems
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Authors
Ross, Michael
Fahroo, Fariba
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Date of Issue
2003
Date
2003
Publisher
Springer
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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.
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Article
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The article of record as published may be located at https://doi.org/10.1007/978-3-540-45056-6_21
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Aeronautics and Astronautics
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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.
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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.