In this paper we address the problem of tracking control of nonlinear systems via contraction analysis. The necessary conditions of the systems which can achieve universal asymptotic tracking are studied under several different cases. We show the links to the well developed control contraction metric, as well as its invariance under dynamic extension. In terms of these conditions, we identify a differentially detectable output, based on which a simple differential controller for trajectory tracking is designed via damping injection. As illustration we apply to electrostatic microactuators.

中文翻译：

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基于收缩分析的非线性系统跟踪控制的必要条件

在本文中，我们通过收缩分析来解决非线性系统的跟踪控制问题。在几种不同的情况下研究了能够实现通用渐近跟踪的系统的必要条件。我们展示了与完善的控制收缩度量的链接，以及它在动态扩展下的不变性。根据这些条件，我们确定了一个可差分检测的输出，在此基础上，通过阻尼注入设计了一个用于轨迹跟踪的简单差分控制器。作为说明，我们适用于静电微致动器。