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

在这项研究中，我们讨论了定义在环上的最强不可证伪模型(简称MPUM)理论的基本问题，它是被数据或轨迹所证明的最强不可证伪模型，是最接近实际动力系统的模型。具体地说，基于一种称为核表示的数学模型，我们主要获得了以下结果。给出了利用给定数据对不稳定系统进行内插的方法和理论问题。我们还给出了多维系统的可达性分析的基本原理，多维系统也是由环定义的系统的重要类别之一，与传统的一维系统一样。我们还在未证伪的控制框架下给出了一些关于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.