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arXiv · 2403.07707

Tight Bounds on Polynomials and Its Application to Dynamic Optimization Problems

Eduardo M. G. Vila·Eric C. Kerrigan·Paul Bruce
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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.

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Eduardo M. G. Vila, Eric C. Kerrigan, Paul Bruce. 2024-03-12. Tight Bounds on Polynomials and Its Application to Dynamic Optimization Problems. https://doi.org/10.1109/tac.2026.3678437

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