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Tight Bounds on Polynomials and Its Application to Dynamic Optimization Problems
Published 12 Mar 2024 in math.OC, cs.SY, and eess.SY | (2403.07707v3)
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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