Peak Estimation of Rational Systems using Convex Optimization

Jared Miller; Roy S. Smith

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arXiv · 2311.08321

Peak Estimation of Rational Systems using Convex Optimization

Jared Miller·Roy S. Smith

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Abstract

This paper presents algorithms that upper-bound the peak value of a state function along trajectories of a continuous-time system with rational dynamics. The finite-dimensional but nonconvex peak estimation problem is cast as a convex infinite-dimensional linear program in occupation measures. This infinite-dimensional program is then truncated into finite-dimensions using the moment-Sum-of-Squares (SOS) hierarchy of semidefinite programs. Prior work on treating rational dynamics using the moment-SOS approach involves clearing dynamics to common denominators or adding lifting variables to handle reciprocal terms under new equality constraints. Our solution method uses a sum-of-rational method based on absolute continuity of measures. The Moment-SOS truncations of our program possess lower computational complexity and (empirically demonstrated) higher accuracy of upper bounds on example systems as compared to prior approaches.

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BibTeX RIS

Jared Miller, Roy S. Smith. 2024-03-25. Peak Estimation of Rational Systems using Convex Optimization. https://arxiv.org/abs/2311.08321

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