AI 中文总结
该研究针对连续时间MIMO系统，通过表征滤波向量的固有维度提取简化滤波向量，开发无模型输出反馈迭代方程，提升LQR控制器性能。
AI 中文摘要
本文研究利用滤波输入输出数据，针对具有n维状态、m维输入和p维输出的连续时间线性系统的无模型输出反馈线性二次调节（LQR）问题。由于系统状态不可用，现有方法依赖动态滤波器，通过可测量的输入输出信号对隐藏状态进行参数化。然而，基于滤波器的参数化的固有维度可能小于完整滤波向量的维度，这种确定性冗余会导致贝尔曼回归秩亏。我们表征了该固有维度，表明对于单输入多输出（SIMO）系统，常规滤波向量仅包含2n个独立分量；对于一般多输入多输出（MIMO）系统，包含n(m+1)个独立分量。基于该表征，从数据中直接提取简化滤波向量，用于开发简化的无模型输出反馈策略迭代和值迭代方程，消除冗余方向、减少未知参数数量，同时保留完全基于输入输出数据的实现。数值示例说明了秩简化及学习到的控制器的有效性。
英文摘要
This article studies model-free output feedback linear quadratic regulation (LQR) for continuous-time linear systems with an $n$-dimensional state, an $m$-dimensional input, and a $p$-dimensional output, using filtered input--output data. Since the system state is unavailable, existing methods rely on dynamic filters to parameterize the hidden state using measurable input--output signals. However, the intrinsic dimension of the resulting filter-based parametrization can be smaller than the dimension of the complete filtered vector, and this deterministic redundancy can make the Bellman regressions rank deficient. We characterize this intrinsic dimension and show that the conventional filtered vector contains only $2n$ independent components for single-input multi-output (SIMO) systems and $n(m+1)$ independent components for general multi-input multi-output (MIMO) systems. Based on this characterization, a reduced filtered vector is extracted directly from data and used to develop reduced model-free output feedback policy iteration and value iteration equations, eliminating the redundant directions and decreasing the number of unknown parameters while retaining a fully input--output data-based implementation. A numerical example illustrates the rank reduction and the effectiveness of the learned controller.
Comments22 pages, 3 figures, 1 table
