Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Sehnalová, Karolína
Institution: Czech Technical University in Prague
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1935710221, G8140083606, G836796558
OpenAlex ID: W7223010196