Appointed-Time Leader-Following Consensus for Second-Order Multi-Agent Systems with Prescribed Performance Guarantees

The appointed-time leader-following consensus problem for second-order multi-agent systems with external disturbance on directed graphs is addressed. A distributed controller based on the cumulative position difference and cumulative velocity difference is proposed, which does not require prior knowledge of external disturbances. It is shown that the proposed controller guarantees the prescribed performance of the controlled systems, namely, to keep the cumulative position difference within a predefined boundary envelope. Furthermore, by employing a novel performance function, it is ensured that the position tracking error converges to an arbitrarily small expected region within the appointed time. Different from most existing finite/fixed-time control methods, here the settling time and the convergence region can both be predefined, which are also independent of initial conditions and the system parameters. Finally, the theoretical results are verified by simulations.