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.

中文翻译：

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领导者和跟随者的编队控制以及规定的绩效保证

本文解决了使用指定的绩效策略以分布式方式为领导者-跟随者多代理系统实现基于位置的相对编队控制的问题。一阶和二阶案例都得到了处理，并且引入了领导者跟随者框架，这是因为选择了一组具有外部输入的代理作为领导者，以便以整个系统实现的方式驱动跟随者群体。在某些规定的性能瞬变范围内的目标编队。在树形图的假设下，当性能函数的衰减率在足够范围内时，针对一阶情况提出了一种分布式控制律。然后，研究了可以具有其他跟随者的两类树图。对于二阶情况 我们提出了一种基于Backstepping方法的分布式控制律，以使领导小组能够在规定的性能范围内引导整个系统实现目标形成。最后，给出了几个仿真示例来说明结果。