Affine formation maneuver tracking control of multiple second-order agents with time-varying delays

This paper considers an affine maneuver tracking control problem for leader-follower type second-order multi-agent systems in the presence of time-varying delays, where the interaction topology is directed. Using the property of the affine transformation, this paper gives the sufficient and necessary conditions of achieving the affine localizability and extends it to the second-order condition. Under the (n + 1)-reachable condition of the given n-dimensional nominal formation with n + 1 leaders, a formation of agents can be reshaped in arbitrary dimension by only controlling these leaders. When the neighboring positions and velocities are available, a formation maneuver tracking control protocol with time-varying delays is constructed with the form of linear systems, where the tracking errors of the followers can be specified. Based on Lyapunov-Krasovskii stability theory, sufficient conditions to realize affine maneuvers are proposed and proved, and the unknown control gain matrix can be solved only by four linear matrix inequalities independent of the number of agents. Finally, corresponding simulations are carried out to verify the theoretical results, which show that these followers can track the time-varying references accurately and continuously.