Decaying Sensitivity of the Zero Solution for a Class of Nonlinear Optimal Control Problems

Titelangaben

Grüne, Lars ; Sperl, Mario:
Decaying Sensitivity of the Zero Solution for a Class of Nonlinear Optimal Control Problems.
In: 27th International Symposium on Mathematical Theory of Networks and Systems MTNS 2026. - Waterloo, Ontario , 2026 . - S. 103-108
DOI: https://doi.org/10.1016/j.ifacol.2026.09.018

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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 localized perturbation of the zero reference leads to an optimal trajectory that decays exponentially with the graph distance. The analysis, based on a nonlinear 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.