Tight bounds on polynomials and its application to dynamic optimization problems
File(s)
Accepted version
Author(s)
Vila, Eduardo
Kerrigan, Eric
Bruce, Paul
Type
Journal Article
Abstract
—This paper presents a pseudo-spectral method for
Dynamic Optimization Problems (DOPs) that allows for tight
polynomial bounds to be achieved via flexible sub-intervals.
The proposed method not only rigorously enforces inequality constraints, but also allows for a lower cost in comparison with non-flexible discretizations. Two examples are provided to demonstrate the feasibility of the proposed method to solve optimal control problems. Solutions to the example problems exhibited up to a tenfold reduction in relative cost.
Dynamic Optimization Problems (DOPs) that allows for tight
polynomial bounds to be achieved via flexible sub-intervals.
The proposed method not only rigorously enforces inequality constraints, but also allows for a lower cost in comparison with non-flexible discretizations. Two examples are provided to demonstrate the feasibility of the proposed method to solve optimal control problems. Solutions to the example problems exhibited up to a tenfold reduction in relative cost.
Date Issued
2026-08-01
Date Acceptance
2026-03-09
Citation
IEEE Transactions on Automatic Control, 2026, 71 (8), pp.5612-5619
ISSN
0018-9286
Publisher
Institute of Electrical and Electronics Engineers
Start Page
5612
End Page
5619
Journal / Book Title
IEEE Transactions on Automatic Control
Volume
71
Issue
8
Copyright Statement
Copyright © 2026 IEEE. All rights reserved, including rights for text and data mining, and training of artificial intelligence and similar technologies. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Publication Status
Published
Date Publish Online
2026-03-30