Robust Spherical Formation Tracking Control of First-order Agents with An Adaptive Neural Flow Estimate

This paper addresses the robust cooperative control for lateral formation tracking a set of circles on the given sphere in an absolutely unknown spatial flowfield. Different from the adaptive estimation method for the unknown flow speed with knowledge of the velocity direction in the literatures, a novel adaptive neural estimate is constructed based on the neighbors' information to approximate the unknown flow velocity. It is noted that such neighbor-based adaptive neural estimation develops the traditional adaptive neural approach by consensus. Then, a robust spherical formation tracking control law is established according to flow estimation. The uniform ultimate boundedness is proven when the communication topology associated with networked first-order agents. The effectiveness of the analytical results is verified by numerical simulations.