基于输入状态数据和多面体互协方差噪声界的数据驱动控制的信息性条件
Informativity conditions for data-driven control based on input-state data and polyhedral cross-covariance noise bounds
摘要：
动力系统的建模和控制依赖于包含系统信息的测量数据。有限的数据测量通常导致一组未伪造的系统模型，即，解释了这些数据。二次性能镇定或控制的数据信息性问题涉及到控制器的存在性，该控制器使所有未伪造的系统镇定或实现期望的二次性能。最近的研究结果在文献中提供的信息量条件的基础上控制的输入状态数据和椭球噪声的界限，如能量或幅度的界限。在本文中，我们考虑的信息量的输入状态数据的控制噪声边界定义通过交叉协方差的噪声相对于一个工具变量，边界最初作为噪声特性的参数边界识别。所考虑的互协方差界被定义为有限数量的超平面，这导致一个（可能无界）多面体集的非伪造系统。我们提供信息性条件的输入状态数据与多面体交叉协方差界稳定和$\mathcal{H}_2$ / $\mathcal{H}_\infty$控制通过顶点/半空间表示的多面体集的未伪造的系统。
英文摘要：
Modeling and control of dynamical systems rely on measured data, which contains information about the system. Finite data measurements typically lead to a set of system models that are unfalsified, i.e., that explain the data. The problem of data-informativity for stabilization or control with quadratic performance is concerned with the existence of a controller that stabilizes all unfalsified systems or achieves a desired quadratic performance. Recent results in the literature provide informativity conditions for control based on input-state data and ellipsoidal noise bounds, such as energy or magnitude bounds. In this paper, we consider informativity of input-state data for control where noise bounds are defined through the cross-covariance of the noise with respect to an instrumental variable; bounds that were introduced originally as a noise characterization in parameter bounding identification. The considered cross-covariance bounds are defined by a finite number of hyperplanes, which induce a (possibly unbounded) polyhedral set of unfalsified systems. We provide informativity conditions for input-state data with polyhedral cross-covariance bounds for stabilization and $\mathcal{H}_2$/$\mathcal{H}_\infty$ control through vertex/half-space representations of the polyhedral set of unfalsified systems.
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