基于循环重构的多速率系统辨识与多面体不确定性建模
Cyclic Reformulation-Based Identification and Polytopic Uncertainty Modeling for Multirate Systems
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中文总结 AI 辅助
研究多速率系统辨识问题，基于循环重构提出非迭代方法，将多速率数据转换生成参数集，用于构建降噪标称模型和多面体不确定性模型，经数值模拟验证，该方法能有效关联系统辨识与不确定性建模。
中文摘要 AI 辅助
现代控制系统越来越依赖不同采样率的异构传感器，间歇性缺失输出给系统辨识带来挑战。本文提出一种基于循环重构的非迭代、面向控制的多速率系统辨识方法。该方法将多速率数据转换为扩展的时不变表示，从单个输入 - 输出数据集生成M个参数集，M为传感器采样周期的最小公倍数。这些参数集有两种互补用途：质心用作降噪标称模型，凸包给出与基于顶点的LMI鲁棒控制设计兼容的多面体不确定性模型。基于作者先前工作的无噪声结构恢复定理，本文引入从M个参数集导出的质心和多面体模型；有限噪声行为通过数值评估。数值模拟支持这两种模型：一个SISO示例表明质心比最佳单个顶点有更高的验证FIT，且大幅优于基于插值的基线；一个MIMO多速率传感示例表明构建的多面体包含的模型即使在最高测试噪声水平下平均验证FIT也超过95%。该框架将多速率系统辨识与面向鲁棒控制的不确定性建模联系起来，无需迭代EM型优化。
英文摘要
Modern control systems increasingly rely on heterogeneous sensors operating at different sampling rates, where intermittently missing outputs pose fundamental challenges for system identification. This paper proposes a non-iterative, control-oriented identification method for multirate systems based on cyclic reformulation. The method transforms multirate data into an expanded time-invariant representation and yields M parameter sets from a single input-output dataset, where M is the least common multiple of the sensor sampling periods. These parameter sets are used in two complementary ways: their centroid serves as a noise-reduced nominal model, while their convex hull gives a polytopic uncertainty model compatible with vertex-based LMI robust control design. Building on the noise-free structural recovery theorem of the authors' preceding work, which is restated here in the notation of the present paper, the present paper newly introduces the centroid and polytopic models derived from the M parameter sets; finite-noise behavior is treated as an empirical observation and is evaluated numerically. Numerical simulations support both models: an illustrative SISO example shows that the centroid attains higher validation FIT than the best individual vertex and substantially outperforms an interpolation-based baseline, while a MIMO multirate sensing example confirms, in line with the LTI counterpart, that the constructed polytope contains models whose validation FIT exceeds 95\% on average even at the highest tested noise level. The polytope is interpreted cautiously, with finite-noise behavior assessed through output-level validation statistics rather than realization-dependent matrix-coordinate distances. The proposed framework therefore links multirate system identification with robust-control-oriented uncertainty modeling without iterative EM-type optimization.
