This paper studies the inherent connection between dynamic region-following formation control (DRFFC) and distributed average tracking (DAT). We propose a fixed-gain DAT algorithm with robustness to initialization errors for linear multiagent systems, which is capable of achieving DAT with a zero tracking error for a large class of reference signals. In the case that the fixed gain cannot be chosen properly, we present an adaptive control gain design, under which each agent simply chooses its own gain and the restriction on knowing the upper bounds on the reference signals and their inputs is removed. We show that the proposed DAT algorithms can be employed to solve the DRFFC problem. This is an attempt on the applications of DAT algorithms to achieve distributed control; existing works most use DAT as distributed estimation algorithms. For single-integrator, double-integrator, higher-order linear dynamics, we derive the corresponding DRFFC algorithms from the DAT algorithm. Compared with existing DRFFC algorithms, the DAT-based DRFFC algorithms do not require the desired region to have a regular shape and is capable of generating a much richer formation behavior. Numerical examples are also included to show the validity of the derived results.

中文翻译：

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动态区域跟踪编队控制与分布式平均跟踪之间的联系

本文研究了动态区域跟踪编队控制（DRFFC）与分布式平均跟踪（DAT）之间的内在联系。我们提出了一种固定增益的DAT算法，该算法对线性多主体系统的初始化错误具有鲁棒性，对于大类参考信号，该算法能够实现零跟踪误差的DAT。在无法正确选择固定增益的情况下，我们提出了一种自适应控制增益设计，在这种设计下，每个代理都可以简单地选择自己的增益，并且消除了已知参考信号及其输入的上限的限制。我们表明，提出的DAT算法可用于解决DRFFC问题。这是在DAT算法的应用中实现分布式控制的尝试。现有作品大多数使用DAT作为分布式估计算法。对于单积分器，双积分器，高阶线性动力学，我们从DAT算法中导出相应的DRFFC算法。与现有的DRFFC算法相比，基于DAT的DRFFC算法不需要所需的区域具有规则的形状，并且能够生成更丰富的地层行为。数值示例也包括在内，以证明得出的结果的有效性。