A collisionless singular Cucker-Smale model with decentralized formation control

We address the design of decentralized feedback control laws inducing\nconsensus and prescribed spatial patterns over a singular interacting particle\nsystem of Cucker-Smale type. The control design consists of a feedback term\nregulating the distance between each agent and pre-assigned subset of\nneighbours. Such a design represents a multidimensional extension of existing\ncontrol laws for 1d platoon formation control. For the proposed controller we\nstudy consensus emergence, collision-avoidance and formation control features\nin terms of energy estimates for the closed-loop system. Numerical experiments\nin 1, 2 and 3 dimensions assess the different features of the proposed design.\n

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