Finite-Time Adaptive Stabilization of Linear Systems
Finite-Time Adaptive Stabilization of Linear Systems
复制标题
线性系统的有限时间自适应稳定
DOI：
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复制
发表时间：
2019
影响因子：
6.8
通讯作者：
G. Michailidis
中科院分区：
文献类型：
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作者：
Mohamad Kazem Shirani Faradonbeh;Ambuj Tewari;G. Michailidis
具有未知动态的线性系统的镇定是自适应控制中的一个典型问题。由于缺乏对系统参数的了解可能导致系统变得不稳定，因此在调节之前需要自适应稳定程序。因此，自适应镇定需要在有限时间内完成。为了实现这一目标，渐近方法并不是很有帮助。目前只有几个现有的非渐近结果，而且目前还没有一个完整的方法来处理这个问题。本文利用随机线性反馈的新方法，建立了有限时间镇定的高概率保证。我们的结果适用于非常普遍的设置，因为我们仔细选择了一组最小的假设。这些问题包括底层系统的稳定性和限制噪声分布的严重程度。为了得到我们的结果，我们还引入了一些新的概念和技术工具来解决闭环系统矩阵的正则性和不稳定性。
Stabilization of linear systems with unknown dynamics is a canonical problem in adaptive control. Since the lack of knowledge of system parameters can cause it to become destabilized, an adaptive stabilization procedure is needed prior to regulation. Therefore, the adaptive stabilization needs to be completed in finite time. In order to achieve this goal, asymptotic approaches are not very helpful. There are only a few existing nonasymptotic results and a full treatment of the problem is not currently available. In this paper, leveraging the novel method of random linear feedbacks, we establish high probability guarantees for finite-time stabilization. Our results hold for remarkably general settings because we carefully choose a minimal set of assumptions. These include stabilizability of the underlying system and restricting the degree of heaviness of the noise distribution. To derive our results, we also introduce a number of new concepts and technical tools to address regularity and instability of the closed-loop matrix.