Interaction Matrix Based Analysis and Asymptotic Cooperative Control of Multi-agent Systems

In this paper, we investigate a decentralized asymptotic cooperative control problem of multi-agent systems with leader-follower configuration. We firstly develop a new method using a proposed “interaction matrix” for the analysis of cooperation convergence of multi-agent systems, i.e. both consensus of the agents states and trajectory tracking of the whole group can be instantaneously concluded only by observing the minimum eigenvalue of the interaction matrix. For a multi-agent system, the external given desired trajectory can be partially obtained (through sensing or detecting) by the leaders, but higher-order derivatives such as acceleration and jerk of the desired trajectory cannot be obtained. In this case, by using some conventional control methods, the trajectory tracking performance is always not satisfactory when a trajectory varies aggressively w.r.t. time. For the sake of asymptotic tracking of an arbitrary given external trajectory of a multi-agent system, we develop a nonlinear cooperative controller based on the robust integral of signum of cooperative error (RISCE) technique, where the interaction matrix is used. The simulation results show asymptotic convergence of cooperation by using the proposed control, and better performance compared to composited nonlinear feedback based PD (CNF-PD) control.