非线性控制系统一致收敛性的激励持久性
Persistency of excitation for uniform convergence in nonlinear control systems
摘要：
在以前的文章中，我们引入了一类非线性时变系统原点一致吸引的充分条件，它是用激励持续时间（PE）来表示的，PE是适应控制和系统辨识文献中的一个著名概念。我们的条件，称为均匀delta-PE的新颖之处在于，它是专为时间和状态的非线性函数，它使我们能够证明一致的渐近稳定性。本文提出了一个新的u-δ-PE的定义，它在概念上与前人的定义相似，但在技术上与前人的定义不同，并给出了几个有用的刻画。我们在此属性和以前在文献中使用的类似属性之间的连接。我们还表明，当这个条件是必要的和充分的一致（全球）渐近稳定性的一大类非线性时变系统。最后，我们展示了我们的主要结果在前馈系统和具有匹配非线性系统的控制应用中的实用性。
英文摘要：
In previous papers we have introduced a sufficient condition for uniform attractivity of the origin for a class of nonlinear time-varying systems which is stated in terms of persistency of excitation (PE), a concept well known in the adaptive control and systems identification literature. The novelty of our condition, called uniform delta-PE, is that it is tailored for nonlinear functions of time and state and it allows us to prove uniform asymptotic stability. In this paper we present a new definition of u-delta-PE which is conceptually similar to but technically different from its predecessors and give several useful characterizations. We make connections between this property and similar properties previously used in the literature. We also show when this condition is necessary and sufficient for uniform (global) asymptotic stability for a large class of nonlinear time-varying systems. Finally, we show the utility of our main results on some control applications regarding feedforward systems and systems with matching nonlinearities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
