graphons

Optimal Control of Semilinear Graphon Systems

  • Martin T. Köhler
  • Artemi Makarow
  • Christian Kirches
    • Categories Infinite Dimensional Optimization, Network Optimization, Systems governed by Differential Equations Optimization Tags , , ,

    We investigate optimal control of semilinear dynamical systems on asymptotically infinite networks, using the notion of graphons. A graphon represents a limit object of a converging graph sequence and serves as a generalization of a finite graph, enabling a systematic analysis of large-scale networks. We analyze semilinear graphon dynamical systems and establish state convergence along … Read more

    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 , , ,

    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 … Read more