论文标题
通过量化反馈对未知线性系统的数据驱动控制
Data-driven Control of Unknown Linear Systems via Quantized Feedback
论文作者
论文摘要
使用量化反馈的控制是对系统合成的基本方法，通信能力有限。在本文中，我们通过直接数据驱动的控制方法解决了具有对数量化反馈的未知线性系统的稳定问题。通过利用最近开发的矩阵S-胶质，我们证明了存在与数据一致的所有可能的动力学的普通稳定控制器的足够且必要的条件，该动力学以线性矩阵不等式的形式。此外，我们制定半准编程来解决最粗的量化密度。通过建立与状态矩阵不稳定特征值的连接，我们进一步证明了对量化反馈稳定的数据的必要等级条件。最后，我们通过数值示例来验证理论结果。
Control using quantized feedback is a fundamental approach to system synthesis with limited communication capacity. In this paper, we address the stabilization problem for unknown linear systems with logarithmically quantized feedback, via a direct data-driven control method. By leveraging a recently developed matrix S-lemma, we prove a sufficient and necessary condition for the existence of a common stabilizing controller for all possible dynamics consistent with data, in the form of a linear matrix inequality. Moreover, we formulate semi-definite programming to solve the coarsest quantization density. By establishing its connections to unstable eigenvalues of the state matrix, we further prove a necessary rank condition on the data for quantized feedback stabilization. Finally, we validate our theoretical results by numerical examples.
