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Efficient and more accurate representation of solution trajectories in numerical optimal control

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Title: Efficient and more accurate representation of solution trajectories in numerical optimal control
Authors: Nie, Y
Kerrigan, E
Item Type: Journal Article
Abstract: We show via examples that, when solving optimal control problems, representing the optimal state and input trajectory directly using interpolation schemes may not be the best choice. Due to the lack of considerations for solution trajectories in-between collocation points, large errors may occur, posing risks if this solution is to be applied. A novel solution representation method is proposed, capable of yielding a solution of much higher accuracy for the same discretization mesh. This is achieved by minimizing the integral of the residual error for the overall trajectory, instead of forcing the errors to be zero only at collocation points. In this way, the requirement for mesh resolution can be significantly reduced, leaving the problem dimensions relatively small. This particular formulation also avoids some of the drawbacks found in the earlier work of integrated residual minimization, leading to more efficient computations.
Issue Date: 31-Jan-2020
Date of Acceptance: 4-Jun-2019
URI: http://hdl.handle.net/10044/1/70928
DOI: https://dx.doi.org/10.1109/LCSYS.2019.2921704
ISSN: 2475-1456
Publisher: Institute of Electrical and Electronics Engineers
Start Page: 61
End Page: 66
Journal / Book Title: IEEE Control Systems Letters
Volume: 4
Issue: 1
Copyright Statement: © 2019 IEEE. Personal use is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
Keywords: math.OC
math.OC
cs.SY
Publication Status: Published
Online Publication Date: 2019-06-07
Appears in Collections:Electrical and Electronic Engineering
Aeronautics