PreprintCC BY 4.0arXiv
On the Peak Estimation of Scalar Polynomial Systems via Integrability
Abstract
We develop a convergent occupation measure framework for peak estimation of scalar polynomial dynamical systems with no a priori state bound. The key observation is that scalar trajectories satisfy a uniform weighted integrability bound whose exponent precisely compensates for the singularity introduced by polynomial compactification. This yields a finite measure formulation with polynomial data. We establish a superposition principle for the resulting weighted continuity equation, prove no relaxation gap and establish convergence of the associated moment-sum-of-squares hierarchy.
Related
- A Polynomial-Time Test for Peak-Oriented Rationalizability
- Integrability of the deformed Toda systems
- On the Local boundedness and higher integrability for the subcritical doubly nonlinear parabolic systems
- Integrability for conformally symplectic systems
- Partial Breakdown of Integrability in Nearly Integrable Systems
BibTeX
@misc{sehnalova2026peak,
title = {{On the Peak Estimation of Scalar Polynomial Systems via Integrability}},
author = {Karolína Sehnalová},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26132},
eprint = {2610.26132},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26132},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Peak Estimation of Scalar Polynomial Systems via Integrability
AU - Karolína Sehnalová
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26132
UR - https://arxiv.org/abs/2610.26132
AB - We develop a convergent occupation measure framework for peak estimation of scalar polynomial dynamical systems with no a priori state bound. The key observation is that scalar trajectories satisfy a uniform weighted integrability bound whose exponent precisely compensates for the singularity introduced by polynomial compactification. This yields a finite measure formulation with polynomial data. We establish a superposition principle for the resulting weighted continuity equation, prove no relaxation gap and establish convergence of the associated moment-sum-of-squares hierarchy.
ER -