发表机构
Rutgers University–New Brunswick（罗格斯大学新布朗斯维克分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于量化数据的数据驱动控制方法，通过两阶段设计（构建SDP和基于李雅普诺夫的量化器更新）实现未知线性系统的指数镇定，并保证量化单元数量有限。
AI 中文摘要
本文研究了仅使用取值于有限集合的量化状态测量值，对未知离散时间线性系统进行数据驱动镇定。所提出的方法包含两个阶段。在控制器设计阶段，我们在保持规定的量化误差界的同时收集量化数据，并利用这些数据构建半定规划（SDP）。我们建立了一个可验证的条件，在该条件下，SDP的任何可行解都能产生镇定的反馈增益，并证明当量化误差足够小时，总能获得镇定的增益。在镇定阶段，我们开发了一种基于李雅普诺夫的量化器更新规则，以保证在量化状态反馈下实现指数收敛。一个关键特征是，量化单元的数量在两个阶段中均保持有限，并在镇定过程中保持不变。仿真结果验证了所提方法的有效性。
英文摘要
This paper studies data-driven stabilization of unknown discrete-time linear systems using only quantized state measurements that take values in finite sets. The proposed approach consists of two stages. In the controller design stage, we collect quantized data while maintaining a prescribed quantization error bound and use them to formulate a semidefinite program (SDP). We establish a verifiable condition under which any feasible solution to the SDP yields a stabilizing feedback gain, and show that a stabilizing gain can always be obtained when the quantization error is sufficiently small. In the stabilization stage, a Lyapunov-based quantizer update rule is developed to guarantee exponential convergence under quantized state feedback. As a key feature, the number of quantization cells remains finite in both stages and constant during stabilization. Simulation results illustrate the effectiveness of the proposed approach.
