Tight Bounds on Polynomials and Its Application to Dynamic Optimization Problems
Optimization and Control
2026-04-08 v4 Systems and Control
Systems and Control
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.
Cite
@article{arxiv.2403.07707,
title = {Tight Bounds on Polynomials and Its Application to Dynamic Optimization Problems},
author = {Eduardo M. G. Vila and Eric C. Kerrigan and Paul Bruce},
journal= {arXiv preprint arXiv:2403.07707},
year = {2026}
}
Comments
Accepted to IEEE Transactions on Automatic Control