AI 中文总结
针对非线性系统数据驱动预测控制问题，提出通过加权范数正则化纳入数据列偏好的框架，使预测器局部化且不丢数据，在保留数据矩阵及其秩时匹配或优于硬数据选择方案，保证了可行性。
AI 中文摘要
数据驱动控制方法如数据赋能预测控制（DeePC）常用于线性系统，通过威廉姆斯基本引理从局部数据推断全局行为。但该原理不适用于非线性系统，其动态特性在不同运行区域会变化。我们提出一种针对非线性系统的数据驱动预测控制框架，通过加权范数正则化纳入数据列偏好，使预测器局部化且不丢弃任何数据。展示了加权方案如何诱导与运行点相关的数据优先级，并确保优化问题适定。对非线性双罐系统的数值研究表明，该方法在保留完整数据矩阵及其秩的同时匹配或优于硬数据选择方案，保证了可行性。
英文摘要
Data-driven control methods, like Data-enabled Predictive Control (DeePC), are often formulated for linear systems, where the principle of superposition allows global system behavior to be inferred from locally collected data through Willems' fundamental lemma. This principle does not hold for nonlinear systems, whose dynamics may vary across operating regions. We propose a data-driven predictive control framework for nonlinear systems that incorporates data column preferences according to their proximity to the current operating point through a weighted norm regularization, thereby localizing the predictor without discarding any data. We show how the proposed weighting scheme induces operating point-dependent data prioritization and ensures a well-posed optimization problem. A numerical study on a nonlinear two-tank system demonstrates that the proposed method matches or outperforms hard data-selection schemes while retaining the full data matrix and its rank, thereby guaranteeing feasibility.
Comments7 pages, 3 figures
