Distributed Finite-time Error Constrained Tracking Control for Multiple Euler-Lagrange Systems

In this paper, distributed finite-time error constrained tracking control for multiple Euler-Lagrange systems is investigated under directed topology. It is considered that the information of the leader is available to only a subset of the followers. A tan-type barrier Lyapunov function (BLF) is utilized to demonstrate that the tracking errors would not exceed the assigned bound. Using backstepping design method, a novel distributed finite-time error constrained tracking protocol is proposed. It is proved that the tracking error of each follower is ultimately bounded in finite time by graph theory, Lyapunov theory, and finite-time stability theory. Numerical simulations demonstrate the effectiveness of the control law.