Agenda

Titolo completo: Dangerous tangents: an application of Gamma-convergence to the control of dynamical systems

Co-autori: Rosario Maggistro, Marco Tolotti

Abstract:We show that the attempt to control some parametric dynamical systems based on a large population of interacting agents can lead to ill-posed optimization problems. When the objective function depends on the steady state, the problem arises in the presence of a tangency condition and a saddle-node bifurcation. To circumvent this theoretical and numerical issue, we propose an asymptotic approach based on Gamma-convergence and show that a mean regularized sequence of auxiliary finite-dimensional problems (Gamma-)converges to the value where the supremum of the ill-posed original problem is reached. We illustrate our point through the riot example analyzed in Granovetter (1978), assuming that a mastermind aims at igniting a massive uprising with maximal cost-efficiency.