Time-varying formation finite-time tracking control for multi-UAV systems under jointly connected topologies

The purpose of this paper is to investigate the time-varying finite-time formation tracking control problem for multiple unmanned aerial vehicle systems under switching topologies, where the states of the unmanned aerial vehicles need to form desired time-varying formations while tracking the trajectory of the virtual leader in finite time under jointly connected topologies.

A consensus-based formation control protocol is constructed to achieve the desired formation. In this paper, the time-varying formation is specified by a piecewise continuously differentiable vector, while the finite-time convergence is guaranteed by utilizing a non-linear function. Based on the graph theory, the finite-time stability of the close-loop system with the proposed control protocol under jointly connected topologies is proven by applying LaSalle’s invariance principle and the theory of homogeneity with dilation.

The effectiveness of the proposed protocol is verified by numerical simulations. Consequently, the proposed protocol can successfully achieve the predefined time-varying formation in finite time under jointly connected topologies while tracking the trajectory generated by the leader.

This paper proposes a solution to simultaneously solve the control problems of time-varying formation tracking, finite-time convergence, and switching topologies.