Energy-Limited Time-Varying Formation Control for Second-Order Multiagent Systems

The energy-limited time-varying formation (ETVF) control problem of second-order multiagent systems (MAS) is addressed for both leaderless and leader-following communication topologies in this paper. Different from the previous results, the joint consideration of energy limitation and formation design is more challenging and practical. First, an ETVF control protocol is presented, and the total energy supply is pregiven and limited, which is more common in practical applications. Then, by an orthogonal transformation, the formation control problem is converted into the consensus stabilization problem for second-order leaderless MAS, where sufficient conditions for the ETVF are derived by joint design of control gains and the total energy. At the same time, the explicit formula that forms the formation center function is obtained to depict the macroscopic movement of the multiagent system as a whole. Moreover, the proposed method is also extended to the leader-following communication structure. Finally, two examples are given to verify the effectiveness of our theoretical results.