Distributed finite-time event-triggered formation control based on a unified framework of affine image

Dear Editor, This letter concentrates on distributed event-triggered formation control problems with finite-time convergence in an arbitrarily dimensional Euclidean space. A new unified approach of finite-time event-triggered formation control is proposed by steering all agents to a sliding manifold (the affine image) to achieve general formations, like affine, rigid or translational formation. It only requires to design an extra steering law driving at least d +1 leaders from an affine image to a rigid or translational image, where d is the dimension of the space. The event-triggered function is designed in a distributed and discontinuous manner based only on local information to reduce the communication and calculation resources by aperiodic sampling. In the proposed event-triggered formation law, zeno-free behavior is ensured.