Recent studies highlight the importance of persistently exciting condition in single signal sequence for model identification and data-driven control methodologies. However, maintaining prolonged excitation in control signals introduces significant challenges, as continuous excitation can reduce the lifetime of mechanical devices. In this paper, we introduce three informativity conditions for various types of multi-signal data, each augmented by weight factors. We explore the interrelations between these conditions and their rank properties in linear time-invariant systems. Furthermore, we introduce open-loop experimental design methods tailored to each of the three conditions, which can synthesize the required excitation conditions either offline or online, even in the presence of limited information within each signal segment. We demonstrate the effectiveness of these informativity conditions in least-squares identification. Additionally, all three conditions can extend Willems' fundamental lemma and are utilized to assess the properties of the system. Illustrative examples confirm that these conditions yield satisfactory outcomes in both least-squares identification and the construction of data-driven controllers.

翻译：近期研究强调了单信号序列中持续激励条件对于模型辨识与数据驱动控制方法的重要性。然而，在控制信号中维持长时间激励会带来显著挑战，因为持续激励可能缩短机械装置的使用寿命。本文针对多种类型的多信号数据，分别引入三种信息性条件，每种条件均通过权重因子进行增强。我们在线性时不变系统中探讨了这些条件之间的相互关系及其秩特性。此外，我们针对三种条件分别提出了开环实验设计方法，这些方法能够在离线或在线状态下合成所需的激励条件，即使在每个信号段内信息有限的情况下也能实现。我们通过最小二乘辨识验证了这些信息性条件的有效性。同时，所有三种条件均可扩展维勒姆斯基本引理，并用于评估系统特性。示例分析表明，这些条件在最小二乘辨识与数据驱动控制器构建中均能取得令人满意的结果。