Fast finite-time consensus of a class of high-order uncertain nonlinear systems

This paper poses and solves a new problem of consensus control where the task is to make the fixed-topology multi-agent network, with each agent described by an uncertain nonlinear system in chained form, to reach consensus in a fast finite time. Our development starts with a set of new sliding mode surfaces. It is proven that, on these sliding mode surfaces, consensus can be achieved if the communication graph has the proposed directed spanning tree. Next, we introduce the multi-surface sliding mode control to drive the sliding variables to the sliding mode surfaces in a fast finite time. The control Lyapunov function for fast finite time stability, motivated by the fast terminal sliding mode control, is used to prove the reachability of the sliding mode surface. A recursive design procedure is provided, which guarantees the boundedness of the control input.