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Further Results on Leader-follower Multi-agent Formation Control with Prescribed Performance Guarantees

Distributed formation control for leader-follower multi-agent systems under prescribed performance guarantees is addressed in this paper. Leader-follower is meant in the sense that a group of agents with external inputs are selected as leaders in order to drive the group of followers in a way that the entire system can achieve the target relative position-based formation within certain prescribed performance transient bounds. In previous work, we have proposed a distributed control law for tree graphs to achieve consensus within certain prescribed transient performance when the decay rate of the performance functions is within a sufficient bound. In this paper, we further discuss the general graphs with cycles. Some necessary conditions on the graph topology are proposed in order to achieve the target formation while satisfying the prescribed performance bounds. We also discuss the roles of the cycles for the convergence benefits in this leader-follower framework. Finally, we illustrate the results with the simulation examples.