A collisionless singular cucker-smale model with decentralized formation control

We address the design of decentralized feedback control laws inducing consensus and prescribed spatial patterns over a singular interacting particle system of Cucker-Smale type. The control design consists of a feedback term regulating the distance between each agent and preassigned subset of neighbors. Such a design represents a multidimensional extension of existing control laws for 1D platoon formation control. For the proposed controller, we study consensus emergence, collision-avoidance, and formation control features in terms of energy estimates for the closed-loop system. Numerical experiments in 1, 2, and 3 dimensions assess the different features of the proposed design.