Finite-Time Consensus for Systems with Second-Order Uncertain Dynamics Under Undirected Topology

Abstract

In Chap. 7, we have explicitly addressed the finite-time leaderless consensus control problem of nonlinear MAS with second-order dynamics in the presence of unknown time-varying gain and non-parametric uncertainties under the local and undirected communication condition. By considering that in most practical applications, the networked communication among the subsystems is not only local but also not bidirectional, and it is highly desirable to consider the local and one-way directed communication condition. For agents with second-order dynamics in the presence of non-parametric uncertainties under local and one-way directed communication topology, the finite-time leaderless consensus control problem is interesting and also challenging, worthy of further studying. Compared with the control results derived in Chap. 7, the finite-time leaderless consensus of second-order nonlinear MAS with non-parametric uncertainties under one-way directed communication topology is much more challenging, where the one-way directed communication topology obviously complicates the underlying problem significantly. This is mainly because the symmetric property does not hold for the directed Laplacian, which imposes a significant technique challenge to extend the existing finite-time adaptive consensus control methods derived from undirected graph to directed graph. In this chapter, we attempt to provide a solution to this problem under directed graph topology.