Extremum seeking-based tracking for unknown systems with unknown control directions
Extremum seeking-based tracking for unknown systems with unknown control directions
复制标题
控制方向未知的未知系统的基于极值搜索的跟踪
DOI：
10.1109/cdc.2012.6426821
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
M. Krstić
中科院分区：
文献类型：
--
作者：
A. Scheinker;M. Krstić
针对一类未知的线性和非线性系统，我们设计了用于轨迹跟踪的控制器。在线性情况下，我们假设未知的时变输入向量在足够短的窗口内满足激励的持久性条件。在多输入非线性情况下，未知时变输入矩阵的平方有一个已知的下界。我们的设计并不保证完美地调节到期望的轨迹，但确保了误差系统的半全局一致最终有界性，并防止了即使在控制方向的初始估计错误的情况下的大超调。稳定性分析的灵感来自于Dürr，Stankovic和Johansson最近工作中的方法，该方法将Gurvits和Li的李括号二阶平均结果与Moreau和Aeyels的摄动理论半全局实用稳定性结果相结合。
We develop controllers which perform trajectory tracking for a class of unknown linear and nonlinear systems. In the linear case we work under the assumption that the time-varying input vector, which is otherwise unknown, satisfies a persistency of excitation condition over a sufficiently short window. In the multi-input nonlinear case the square of the unknown time-varying input matrix has a known lower bound. Our design does not guarantee perfect regulation to the desired trajectory, but ensures semiglobal uniform ultimate boundedness of the error system and prevents large overshoots even when the initial estimate of the control direction is wrong. The stability analysis is inspired by the approach in a recent work by Dürr, Stankovic, and Johansson, which combines a Lie bracket second-order averaging result of Gurvits and Li with an extension of the perturbation theory semiglobal practical stability result of Moreau and Aeyels.