Formation control and lag formation control for human–machine interaction second-order multiagent systems

In this paper, the formation control and lag formation control problems for second-order multiagent systems (MASs) with and without nonlinear intrinsic dynamics are discussed, in which a fraction of agents are controlled by humans and the others are free from human intervention. By selecting suitable control protocol and Lyapunov functional, a formation criterion for the second-order nonlinear MAS is derived. Furthermore, considering that time delay always exists between agent and virtual leader due to finite transmission speed, a lag formation criterion for the second-order nonlinear MAS is also obtained by selecting appropriate control strategy. In addition, the above obtained results are further extend to the double-integrator MAS. Finally, the devised control strategies are verified by exploiting two numerical examples.