In this paper, a distributed average tracking (DAT) problem is studied for Lipschitz-type of nonlinear dynamical systems. The objective is to design DAT algorithms for locally interactive agents to track the average of multiple reference signals. Here, in both dynamics of agents and reference signals, there is a nonlinear term satisfying a Lipschitz-type condition. Three types of DAT algorithms are designed. First, based on state-dependent-gain design principles, a robust DAT algorithm is developed for solving DAT problems without requiring the same initial condition. Second, by using a gain adaption scheme, an adaptive DAT algorithm is designed to remove the requirement that global information, such as the eigenvalue of the Laplacian and the Lipschitz constant, is known to all agents. Third, to reduce chattering and make the algorithms easier to implement, a couple of continuous DAT algorithms based on time-varying or time-invariant boundary layers are designed, respectively, as a continuous approximation of the aforementioned discontinuous DAT algorithms. Finally, some simulation examples are presented to verify the proposed DAT algorithms.

中文翻译：

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Lipschitz 型非线性动力系统的分布式平均跟踪


本文研究了Lipschitz型非线性动力系统的分布式平均跟踪（DAT）问题。目标是为本地交互代理设计 DAT 算法，以跟踪多个参考信号的平均值。这里，在代理和参考信号的动力学中，都存在满足 Lipschitz 型条件的非线性项。设计了三种类型的DAT算法。首先，基于状态相关增益设计原理，开发了一种鲁棒的DAT算法来解决DAT问题，而不需要相同的初始条件。其次，通过使用增益自适应方案，设计了自适应 DAT 算法，以消除所有代理都知道全局信息（例如拉普拉斯算子的特征值和 Lipschitz 常数）的要求。第三，为了减少抖振并使算法更容易实现，分别设计了几种基于时变或时不变边界层的连续DAT算法，作为上述不连续DAT算法的连续逼近。最后，给出了一些仿真例子来验证所提出的DAT算法。