Robust fixed-time formation control for quadrotor unmanned aerial vehicles with directed topology

Formation control is one of the key technologies for multiple unmanned aerial vehicles (UAVs). Compared with asymptotic or finite-time controllers, fixed-time controller can provide a guaranteed settling time, which does not depend on initial conditions and is an appealing property for controller design. Thus, robust fixed-time formation controller design for quadrotor UAVs under external disturbance and directed topology is investigated in this paper. A multi-variable super-twisting like integral sliding mode surface and a disturbance observer are respectively designed for position and attitude loops to guarantee robustness. Bi-limit homogeneity is utilized to design the whole closed-loop fixed-time controllers. By skillfully using bi-limit homogeneity technique and Lyapunov theory, the comprehensive stability of position and attitude loops is addressed. Finally, the multiple UAVs are utilized to track a pre-planned trajectory in 3D space and simulation results illustrate that the settling time can be reduced about 40% compared with finite-time controllers.

Cluster Synchronization in a Network of Nonlinear Systems with Directed Topology and Competitive Relationships

This paper studies the cluster synchronization problem of coupled nonlinear systems with directed topology and competitive relationships. We assume that nodes within the same cluster have the same intrinsic dynamics, whereas node dynamics between different clusters differ. In the same cluster, there only exist cooperative relationships, and there may have competitive relationships among nodes belonging to different clusters. Under the assumptions that each node satisfies one-sided Lipschitz condition, and the digraphs of each cluster are strongly connected, some sufficient conditions for cluster synchronization in the cases of linear coupling and nonlinear coupling are obtained respectively. The obtained conditions are presented as some algebraic conditions which are easy to solve. Finally, our results are validated by two numerical simulations.