Robust control strategies for mean-field collective dynamics

The main topic of the thesis is the synthesis of control laws for interacting agent-based dynamics and their mean-field limit. In particular, after a general introduction, in the second chapter a linearization-based approach is used for the computation of sub-optimal feedback laws obtained from the solution of differential matrix Riccati equations. Quantification of dynamic performance of such control laws leads to theoretical estimates on suitable linearization points of the nonlinear dynamics. Subsequently, the feedback laws are embedded into a nonlinear model predictive control framework where the control is updated adaptively in time according to dynamic information on moments of linear mean-field dynamics. The performance and robustness of the proposed methodology is assessed through different numerical experiments in collective dynamics. In the other chapters of the thesis I present some related projects, robustness of systems with uncertainties, a proximal gradient approach for sparse control and an application in crowd evacuation dynamics.