Observer‐Based Affine Formation Maneuver Control of Multi‐Agent Systems With Time Delays

ABSTRACT This paper concentrates on the affine formation maneuver control of linear multi‐agent systems (MASs) containing bounded time delays under directed graphs. For the time delays existing in the followers' communication channels, the predictive observers of followers are introduced to estimate their future states. Two distributed affine formation control protocols are proposed, which correspond to the cases where leaders have constant velocities and time‐varying velocities, respectively. Besides, applying the Linear Matrix Inequality (LMI) and Lyapunov–Krasovskii functional theory, we can obtain the convergence condition for the state estimation. Particularly, for the leaders moving with time‐varying velocities, because the absolute velocity in the traditional control protocol is difficult to measure, we modify a new control protocol based on a velocity estimator to make the control be completed more easily. Applying the control protocols proposed here, the target formation of delayed MASs can be achieved successfully. Finally, corresponding numerical examples are simulated to demonstrate the feasibility of the main theoretical results.