Affine formation maneuver control of delayed second-order multi-agent systems with zero accelerations moving leaders

This paper is devoted to studying the affine formation maneuver control (AFMC) of the second-order linear multi-agent systems (MASs) containing bounded communication delays over directed graphs, in which the accelerations of moving leaders remain zeros. The main objective of this paper is to devise the appropriate control protocol to make the agents in the systems achieve the desired formation. In order to deal with the communication delays existed in the communication channels of followers, the predictive observers play an important role in estimating the future information of positions and velocities for followers. The observer-based control protocol is presented here, which merely requires the relative information of agents rather than global reference frames. Additionally, the convergence conditions for the predictive observers can be guaranteed by utilizing LMIs and Lyapunov-Krasovskii functional theory. Finally, the numerical example is simulated through the software MATLAB to exhibit the feasibility of main theoretical results.