Suboptimal nonlinear feedback control laws for collective dynamics

We present feedback control methodologies for the stabilization of nonlinear collective dynamics. The proposed controllers circumvent the curse of dimensionality associated to dynamic programming of large-scale nonlinear dynamics by means of different structural assumptions on the nonlinearity and the associated Hamilton-Jacobi-Bellman equation. We explore a power series expansion method, and a state-dependent Riccati equation approach. The proposed designs are studied for a relaxed optimal power flow model, and for binary interactions arising in opinion and consensus dynamics.