Non-C2 Lie Bracket Averaging for Nonsmooth Extremum Seekers
Non-C2 Lie Bracket Averaging for Nonsmooth Extremum Seekers
复制标题
非平滑极值搜索器的非 C2 李括号平均
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
M. Krstić
中科院分区：
文献类型：
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作者：
A. Scheinker;M. Krstić
基于极值寻求的控制的一个缺点是在系统动力学中引入了高频振荡，这使得即使是稳定的系统也无法稳定在平衡点上。在本文中，我们开发了基于极值搜索的控制器，它的控制努力与传统的基于极值搜索的方案不同，随着系统趋于平衡而消失。由于我们开发的控制器在原点不可微，在证明我们的控制方案的一种稳定性形式时，我们从一个更一般的问题开始，扩展了Moreau和Aeyels的半全局实际稳定性结果，甚至对于在某一点不可微的系统，也建立了系统与其平均值之间的关系。更具体地说，为了将实际的稳定性结果应用于我们的控制方案，我们将Kurzweil， Jarnik, Sussmann, Liu， Gurvits和Li的Lie支架平均结果推广到非c函数。然后，我们改进了之前关于线性时变单输入系统的模型无关半全局指数实用镇定的结果，假设时变输入向量（否则未知）在足够短的窗口内满足激励条件的持久性。(DOI: 10.1115/1.4025457)
A drawback of extremum seeking-based control is the introduction of a high frequency oscillation into a system’s dynamics, which prevents even stable systems from settling at their equilibrium points. In this paper, we develop extremum seeking-based controllers whose control efforts, unlike that of traditional extremum seeking-based schemes, vanish as the system approaches equilibrium. Because the controllers that we develop are not differentiable at the origin, in proving a form of stability of our control scheme we start with a more general problem and extend the semiglobal practical stability result of Moreau and Aeyels to develop a relationship between systems and their averages even for systems which are nondifferentiable at a point. More specifically, in order to apply the practical stability results to our control scheme, we extend the Lie bracket averaging result of Kurzweil, Jarnik, Sussmann, Liu, Gurvits, and Li to non-C functions. We then improve on our previous results on model-independent semiglobal exponential practical stabilization for linear time-varying single-input systems under the assumption that the time-varying input vector, which is otherwise unknown, satisfies a persistency of excitation condition over a sufficiently short window. [DOI: 10.1115/1.4025457]
DOI：
10.1016/j.automatica.2013.02.016
发表时间：
2011-09
期刊：
Autom.
影响因子：
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作者：
Hans-Bernd Dürr;M. Stanković;C. Ebenbauer;K. Johansson
通讯作者：
Hans-Bernd Dürr;M. Stanković;C. Ebenbauer;K. Johansson