基于数据驱动的未知离散时间线性系统的输出反馈分析与控制
Data-Driven Output Feedback based Analysis and Control for Unknown Discrete-Time Linear System
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中文总结 AI 辅助
本文针对输入矩阵已知的未知离散时间线性系统，提出温和的数据可辨识性条件与直接的状态反馈控制方法，通过参数化观测器将动态输出反馈问题转化为状态反馈问题，实现了渐近逼近LQR解的动态输出控制。
中文摘要 AI 辅助
利用数据可辨识性的概念，现有研究结果已针对未知线性离散时间系统的各类控制问题，给出了数据对控制器设计具有可辨识性的条件，并开发了从数据中计算此类控制器的方法。然而，基于输入输出数据计算动态输出反馈控制律的现有条件较为严苛。本文首先针对输入矩阵已知的未知系统，开展数据可辨识性分析与控制研究。结果表明，此类系统的可辨识性条件温和得多，且计算其镇定、无差拍控制及线性二次调节器（LQR）的状态反馈控制律的方法也更为直接。进一步地，基于参数化观测器，本文证明了未知系统的动态输出反馈控制律计算问题，可转化为输入矩阵已知的辅助系统的状态反馈控制律设计问题。因此，本文第一部分的结果可直接用于基于输入输出数据，计算未知线性离散时间系统的镇定与无差拍控制的动态输出反馈控制律。此外，本文提出了一种动态输出反馈控制律，该控制律将渐近逼近原未知系统的状态反馈LQR解。
英文摘要
Using the notion of data informativity, the existing results have given conditions under which the data are informative for controller designs for various control problems of unknown linear discrete-time systems, and have developed methods to compute such controllers from data. Nevertheless, the existing conditions for computing a dynamic output feedback control law based on the input and output data are somehow stringent. In this paper, we first focus on developing data informativity analysis and control for an unknown system with a known input matrix. It turns out that the informativity conditions for such a system are much milder and the methods for computing state feedback control laws for stabilization, deadbeat control, and the linear-quadratic regulator (LQR) for such a system are much more straightforward. Further, based on the parameterized observer, we show that the problem of computing a dynamic output feedback control law for an unknown system can be converted to the problem of designing a state feedback control law for an ancillary system whose input matrix is known. Therefore, the results of the first part of this paper can be directly used to compute a dynamic output feedback control law for stabilization and deadbeat control for unknown linear discrete-time systems based on the input and output data. Moreover, we present a dynamic output feedback control law which will asymptotically approach a state feedback LQR solution to the original unknown system.
