Controlling discrete semilinear wave equations toward flocks

Abstract: In this work, we initiate the research on controlling nonlinear waves propagating on lattices from a completely new perspective. We consider nonlinear waves on a lattice as a system of interacting particles and study their collective flocking behavior. By designing suitable feedback controls, we show that any admissible flock can be reached within a finite amount of time. Finally, we highlight the connection between our flocking problem and a minimal-time problem in the framework of nonlinear Hamilton-Jacobi equations and optimal control theory.