Tight Bounds on Polynomials and Its Application to Dynamic Optimization Problems
arXiv:2403.07707 · doi:10.1109/TAC.2026.3678437
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.
Accepted to IEEE Transactions on Automatic Control