Decaying Sensitivity of the Zero Solution for a Class of Nonlinear Optimal Control Problems
Optimization and Control
2026-05-19 v2 Dynamical Systems
Abstract
We study spatial decay properties of sensitivities in a nonlinear optimal control problem with a graph-structured interaction topology. For a problem with nonlinear decoupled dynamics and quadratic cost, we show that a perturbation of the zero initial condition at a single node induces an optimal trajectory whose node-wise norms decay exponentially with the graph distance from the perturbed node. The analysis, based on a nonlinear null-controllability condition, provides a first step toward extending known spatial decay results from linear-quadratic to nonlinear systems. A numerical example illustrates the theoretical findings.
Cite
@article{arxiv.2602.05020,
title = {Decaying Sensitivity of the Zero Solution for a Class of Nonlinear Optimal Control Problems},
author = {Lars Grüne and Mario Sperl},
journal= {arXiv preprint arXiv:2602.05020},
year = {2026}
}