On MPUM theory for dynamical systems defined by the rings : Kernel representation approach

在这项研究中，我们解决的理论上的最强大的不可伪造的模型（简称为MPUM）定义的环，这是不可伪造的数据或轨迹的模型，是最接近的模型，以实际的动力系统的基本问题。特别地，基于被称为核表示的数学模型，我们主要获得了以下内容。给出了利用给定数据对不稳定系统进行插值的方法和理论问题。同时也为多维系统的可拓性分析提供了基础，这也是由环定义的系统和传统的一维系统的重要类别之一。我们还提供了一些新的结果，数据驱动的控制器综合的非伪造控制框架。

In this study, we address fundamental issues on the theory of most powerful unfalsified model (which is abbreviated to MPUM)defined on the rings, which is the model unfalsifid by the data or trajectories and is the closest model to the actual dynamical system. Particularly, based on a mathematical model which is called a kernel representation, we mainly obtained the following. We have provided the method and theoretical issues on the problem for unstable systems to be interpolated by using the given data. We have also provided the fundamentals on achievability analysis for multi-dimensional system, which is also one of the important classes of the system defined by the ring as well as conventional 1 dimensional system. We have also provided some new results on data-driven controller synthesis in the unfalsified control framework.