Spherical formation tracking control for second-order agents with unknown general flowfields and strongly connected topologies

This article addresses the problem of directing a family of second-order agents suffering external flowfields to achieve the lateral formation tracking motion on a target sphere. Distinguishing from the existing results based on bidirectional networks, this paper firstly attempts to deal with the fixed directed strongly connected multiagent systems and then the switch directed networks with the strong connectivity of each topology. Both the velocity field (eg, the constant-velocity flowfield, the rotating flowfield, Eulerian specification flowfield, the parameterized flowfield) and the gravitational field are under consideration, where the flow specification is a spatiotemporal variable with an unknown parameter vector. Therefore, it is known as the general flowfield. To access to the fixed network, a new second-order observer for the velocity field as well as an adaptive estimate for the gravitational field are constructed by using the tool of adaptive backstepping in the beginning. They, together with the distributed control laws in the spherical normal, lateral, and longitudinal directions, are proposed to accomplish spherical tracking, circular tracking, and lateral formation. For the purpose of avoiding the overparametrization of observer and reducing the complexity of design, a minimum-order observer is proposed later. Finally, our proposed methods servicing to the fixed topologies are developed to the cases where the switching topologies are directed and each one is strongly connected. The stability of the fixed and directed strongly connected system is investigated based on the Barbalat's lemma, whereas the Lyapunov stability theory of nonsmooth systems is introduced to analyze the stability of the switching cases. Theoretical results are proven by the numerical examples.