Observer-Based Affine Formation Maneuver Control of Second-Order Multi-Agent Systems with Time Delays

This paper is devoted to studying the affine formation maneuver control (AFMC) of the second-order linear multi-agent systems (MASs) containing bounded time delays over directed graphs. In order to deal with the time delays existed in the communication channels of followers, the predictive observers play an important role in estimating the future information of position and velocity for followers. Three distributed control protocols are presented here according to the different cases of accelerations for leaders, i.e. the leaders possess zero accelerations, constant accelerations and time-varying accelerations, respectively. In addition, the key conditions for ensuring the successful observation of the predictive observer can be obtained, by utilizing linear matrix inequalities (LMIs) and Lyapunov–Krasovskii functional theory. Specifically, we also propose the absolute acceleration estimators when leaders have time-varying accelerations, such that the control protocol modified here is easier to enforce. Eventually, three numerical examples are simulated to exhibit the feasibility of main theoretical results.