An adaptive backstepping design for formation tracking motion in an unknown Eulerian specification flowfield

This paper considers the problem of directing second-order agents tracking a family of simple, closed curves and maintaining a spatiotemporal formation in an unknown spatiotemporal flowfield, where the description of flowfield is Eulerian specification that includes almost all of flowfields in the literature (e.g. the uniform, constant wind, the uniform rotating flowfield and the parameterizable flowfield). Adaptive backstepping technology is first applied with our previous geometric extension to construct the robust formation tracking control and then combined with consensus to propose a new adaptive estimator for the unknown flow speed vector. It is proved that the designed cooperative control system is asymptotically stable if the communication topology is connected. Simulation results are given to verify the theoretical analysis.