Leader–Follower Formation Control With Prescribed Performance Guarantees

This article addresses the problem of achieving relative position-based formation control for leader-follower multiagent systems in a distributed manner using a prescribed performance strategy. Both the first- and second-order cases are treated and a leader-follower framework is introduced in the sense that a group of agents with external inputs is selected as leaders in order to drive the group of followers in a way that the entire system achieves a target formation within certain prescribed performance transient bounds. Under the assumption of tree graphs, a distributed control law is proposed for the first-order case when the decay rate of the performance functions is within a sufficient bound. Then, two classes of tree graphs that can have additional followers are investigated. For the second-order case, we propose a distributed control law based on a backstepping approach for the group of leaders to steer the entire system achieving the target formation within the prescribed performance bounds. Finally, several simulation examples are given to illustrate the results.