Distributed control and parameter estimation for homogeneous Lagrangian multi-agent systems

In this paper, we consider the formation control problem for uncertain homogeneous Lagrangian nonlinear multi-agent systems in a leader-follower scheme, under an undirected communication protocol. A distributed adaptive control protocol of minimal complexity is proposed that achieves prescribed, arbitrarily fast and accurate formation establishment between the following agents and the leader as well as the synchronization of the parameter estimates of all following agents. The estimation and control laws are distributed in the sense that the control signal and update laws of each agent are calculated based solely on local relative state information from its neighborhood set. Moreover, provided that the communication graph is connected and contrary to the related works on multi-agent systems, the controller-imposed transient and steady state performance bounds are fully decoupled from: i) the underlying graph topology, ii) the control gains selection and iii) the agents' model uncertainties, and are solely prescribed by certain designer-specified performance functions. Finally, a simulation study with hovercraft platforms clarifies and verifies the approach.