Observer-based finite-time coordinated tracking for high-order integrator systems with matched uncertainties under directed communication graphs

In this paper, we study the finite-time coordinated tracking problem for high-order integrator systems with bounded matched uncertainties. When relative state information of the neighbors is available, a distributed finite-time observer is proposed for each follower which enables a distributed controller design that solves the finite-time coordinated tracking problem under directed switching communication graphs. When only relative output information is available, robust exact differentiators and high-order sliding mode controllers are employed together with the distributed finite-time observers. It is proven that under fixed directed communication graphs, finite-time coordinated tracking can still be achieved. The control input in this case is bounded and quasi-continuous, that is, continuous everywhere except on a manifold. Numerical simulations are provided to illustrate the effectiveness of the proposed control strategies.