投影正则化间接数据驱动预测控制
Projection-Regularized Indirect Data-Driven Predictive Control
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中文总结 AI 辅助
针对间接数据驱动预测控制受过程噪声与数据稀缺影响的问题，提出PRPC方法，经偏差-方差分析、鞅集中不等式推导及仿真验证，实现LTI/LTV系统的鲁棒控制与实时性。
中文摘要 AI 辅助
间接数据驱动预测控制方法常受过程噪声与数据稀缺问题影响。本文提出投影正则化预测控制（PRPC），通过正则化投影保留基本引理权重向量，该投影可解析浓缩为高效的固定维协方差更新。严格的偏差-方差分析证明，与未正则化子空间方法相比，PRPC在过程噪声（变量误差）和结构秩缺陷下严格降低预测误差。利用这些特性，我们开发了针对线性时变（LTV）系统的自适应滑动窗口控制器。为应对闭环数据相关性的安全性问题，我们使用向量值鞅集中不等式推导了经验预测器的一致时间有限样本置信界，将该统计不确定半径嵌入动态收紧的约束集，严格保证高概率下的鲁棒递归可行性与输入-状态实际稳定性（ISpS）。在LTI和LTV基准上的仿真验证了其实时可处理性与严格约束满足性。
英文摘要
Indirect data-driven predictive control methods often suffer under process noise and data scarcity. This paper introduces Projection-Regularized Predictive Control (PRPC), retaining the fundamental-lemma weight vector via a regularized projection analytically condensed into an efficient, fixed-dimension covariance update. A rigorous bias--variance analysis proves PRPC strictly reduces prediction error under process noise (errors-in-variables) and structural rank deficiencies compared to unregularized subspace methods. We leverage these properties to develop an adaptive sliding-window controller for linear time-varying (LTV) systems. To guarantee safety despite closed-loop data correlations, we derive a uniform-in-time, finite-sample confidence bound on the empirical predictor using vector-valued martingale concentration inequalities. Embedding this statistical uncertainty radius into a dynamically tightened constraint set rigorously ensures robust recursive feasibility and Input-to-State practical Stability (ISpS) with high probability. Simulations on LTI and LTV benchmarks demonstrate real-time tractability and strict constraint satisfaction.
