In this article, we consider extremum seeking problems for a general class of nonlinear dynamic control systems. The main result of the article is a broad family of control laws which optimize the steady-state performance of the system. We prove practical asymptotic stability of the optimal steady-state and, moreover, propose sufficient conditions for the asymptotic stability in the sense of Lyapunov. The results generalize and extend existing results which are based on Lie bracket approximations. In particular, our approach does not rely on singular perturbation theory, as commonly used in extremum seeking of nonlinear dynamic systems.

中文翻译：

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使用李括号逼近法对非线性动态系统进行极值搜索控制

在本文中，我们考虑一类一般非线性动态控制系统的极值搜索问题。这篇文章的主要结果是优化系统稳态性能的一系列控制律。我们证明了最优稳态的实用渐近稳定性，此外，还提出了李雅普诺夫意义上的渐近稳定性的充分条件。结果概括和扩展了基于李括号近似的现有结果。特别是，我们的方法不依赖于非线性动态系统的极值寻找中常用的奇异微扰理论。