This paper proposes a fully distributed control protocol that achieves time-varying group formation tracking for linear multiagent systems connected via a directed graph. The group formation tracking often leads to sub-formations especially when the leaders are placed far apart or they have separate control inputs. In the proposed approach, the followers are distributed into several subgroups and each subgroup attains the predefined subformation along with encompassing the leaders. Each subgroup can be assigned multiple leaders, contrary to the single-leader case considered in most existing literature, which makes the current problem nontrivial. When multiple leaders exist in a subgroup, the subformation attained by that subgroup keeps tracking a convex combination of the states of the leaders. A distributed adaptive control protocol has been introduced in this paper which uses only relative state information and, thus, avoids direct computation of the graph Laplacian matrix. Due to the virtue of this, the proposed scheme remains effective even when some of the agents get disconnected from the network due to sudden communication failure. An algorithm is provided to outline the steps to design the control law to attain time-varying group formation tracking with multiple leaders. Toward the end, a case study on multitarget surveillance operation is taken up to show an important application of the proposed adaptive control technique.

中文翻译：

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有向图上具有多个领导者的多主体系统的分布式自适应时变群形成跟踪

本文提出了一种完全分布式的控制协议，该协议可实现通过有向图连接的线性多主体系统的时变组形成跟踪。小组编队跟踪通常会导致子编队，尤其是当领导者相距遥远或他们具有单独的控制输入时。在提出的方法中，关注者被分为几个子组，每个子组都达到了预定义的子形式，并且包含了领导者。与大多数现有文献中考虑的单领导者情况相反，可以为每个子组分配多个领导者，这使得当前的问题变得微不足道。当一个子组中存在多个领导者时，该子组所获得的子形式将保持跟踪领导者状态的凸组合。本文介绍了一种分布式自适应控制协议，该协议仅使用相对状态信息，从而避免了对图拉普拉斯矩阵的直接计算。因此，即使某些代理由于突然的通信故障而与网络断开连接，所提出的方案仍然有效。提供了一种算法，概述了设计控制律的步骤，以实现具有多个领导者的时变组形成跟踪。最后，以多目标监视操作为例，说明所提出的自适应控制技术的重要应用。即使某些代理由于突然的通信故障而与网络断开连接，所提出的方案仍然有效。提供了一种算法，概述了设计控制律的步骤，以实现具有多个领导者的时变组形成跟踪。最后，以多目标监视操作为例，说明所提出的自适应控制技术的重要应用。即使某些代理由于突然的通信故障而与网络断开连接，所提出的方案仍然有效。提供了一种算法，概述了设计控制律的步骤，以实现具有多个领导者的时变组形成跟踪。最后，以多目标监视操作为例，说明所提出的自适应控制技术的重要应用。