Integer Control Approximations for Graphon Dynamical Systems

  • Martin T. Köhler
  • Artemi Makarow
  • Christian Kirches
    • Categories (Mixed) Integer Nonlinear Programming, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , Short URL: https://optimization-online.org/?p=29601
    \(\) Graphons generalize graphs and define a limit object of a converging graph sequence. The notion of graphons allows for a generic representation of coupled network dynamical systems. We are interested in approximating integer controls for graphon dynamical systems. To this end, we apply a decomposition approach comprised of a relaxation and a reconstruction step. We extend the sum-up rounding algorithm to operate on a finite partition of the continuous vertex set in a graphon setting and restore integer feasibility for a given relaxed control solution. Finally, we derive an \( L^1 \) bound for the state variables for structurally similar graphs and approximated integer controls. We verify our claims by simulating the Kuramoto model for large networks.

    Citation

    M. T. Köhler, A. Makarow and C. Kirches, "Integer Control Approximations for Graphon Dynamical Systems," in IEEE Control Systems Letters, doi: 10.1109/LCSYS.2025.3577926.