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

在本研究中，我们讨论了在环上定义的最强大的非证伪模型（缩写为MPUM）理论的基本问题，它是数据或轨迹不可证伪的模型，是最接近实际动力系统的模型。具体来说，基于一种称为核表示的数学模型，我们主要得到了以下结果：给出了不稳定系统用给定数据插值问题的方法和理论问题。本文还提供了多维系统可达性分析的基本原理，多维系统是环所定义的系统的重要类别之一，也是传统的一维系统。在非证伪控制框架下，我们还提供了一些数据驱动控制器综合的新结果。

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.