Saved in:
Bibliographic Details
Main Authors: Miller, Jared, Smith, Roy S.
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2311.08321
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866914727114833920
author Miller, Jared
Smith, Roy S.
author_facet Miller, Jared
Smith, Roy S.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2311_08321
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Peak Estimation of Rational Systems using Convex Optimization
Miller, Jared
Smith, Roy S.
Optimization and Control
Systems and Control
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.
title Peak Estimation of Rational Systems using Convex Optimization
topic Optimization and Control
Systems and Control
url https://arxiv.org/abs/2311.08321