We derive necessary and sufficient conditions for leader-follower multi-agent systems such that we can further apply prescribed performance control to achieve the desired formation while satisfying certain transient constraints. A leader-follower framework is considered 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 target formation within certain prescribed performance transient bounds. We first derive necessary conditions on the leader-follower graph topology under which the target formation together with the prescribed performance guarantees can be fulfilled. Afterwards, the derived necessary conditions are extended to necessary and sufficient conditions for leader-follower formation control under transient constraints. Finally, the proposed results are illustrated with simulation examples.

翻译：我们推导了领导者-跟随者多智能体系统在同时满足某些暂态约束条件下，可进一步应用预设性能控制以实现期望编队的必要且充分条件。考虑一个领导者-跟随者框架，其中一组带有外部输入的智能体被选为领导者，以驱动跟随者群体，使得整个系统能够在满足特定预设性能暂态边界的同时达到目标编队。首先，我们推导了领导者-跟随者图拓扑的必要条件，在此拓扑下目标编队与预设性能保证能够同时实现。随后，将所推导的必要条件扩展为存在暂态约束时领导者-跟随者编队控制的必要且充分条件。最后，通过仿真示例对所提出的结果进行了验证。