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

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.

💡 Research Summary

The paper investigates spatial decay properties of sensitivities in a class of infinite‑horizon optimal control problems that feature a graph‑structured interaction topology. The authors consider a network of s subsystems, each governed by a decoupled nonlinear dynamics
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