Chapter 2 - Robust finite-time leader-following consensus algorithms for second-order multi-agent systems with nonlinear dynamics

Abstract

In this chapter, we consider the robust finite-time consensus problem for leader-following multi-agent systems with second-order nonlinear dynamics. With the help of matrix theory, graph theory, and finite-time control technique we develop continuous distributed control algorithms in a quite unified way for each follower agent. We give a rigorous proof by using Lyapunov stability theory and show that the closed-loop systems are provided with fast finite-time stability and strong robustness against matched (unmatched) uncertainties. We also establish a sufficient condition ensuring robust finite-time leader-following consensus and find that the finite-time is determined by not only the parameters in the control algorithms but also by the initial states of agents in the network. Finally, we employ two examples to illustrate the effectiveness of the theoretical results.