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京都大学 / 新制・課程博士 / 博士(情報学) / 甲第23321号 / 情博第757号 / 新制||情||129(附属図書館) / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 太田 快人, 教授 山下 信雄, 教授 大塚 敏之 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DGAM

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The main purpose of this dissertation is to define and solve problems on optimal sensing and actuating policies in Cyber-Physical Systems (CPSs). Cyber-physical system is a term that was introduced recently to define the increasing complexity of the interactions between computational hardwares and their physical environments. The problem of designing the ``cyber'' part may not be trivial but can be solved from scratch. However, the ``physical'' part, usually a natural physical process, is inherently given and has to be identified in order to propose an appropriate ``cyber'' part to be adopted. Therefore, one of the first steps in designing a CPS is to identify its ``physical'' part. The ``physical'' part can belong to a large array of system classes. Among the possible candidates, we focus our interest on Distributed Parameter Systems (DPSs) whose dynamics can be modeled by Partial Differential Equations (PDE). DPSs are by nature very challenging to observe as their states are distributed throughout the spatial domain of interest. Therefore, systematic approaches have to be developed to obtain the optimal locations of sensors to optimally estimate the parameters of a given DPS. In this dissertation, we first review the recent methods from the literature as the foundations of our contributions. Then, we define new research problems within the above optimal parameter estimation framework. Two different yet important problems considered are the optimal mobile sensor trajectory planning and the accuracy effects and allocation of heterogeneous sensors. Under the remote sensing setting, we are able to determine the optimal trajectories of remote sensors. The problem of optimal robust estimation is then introduced and solved using an interlaced ``online'' or ``real-time'' scheme. Actuation policies are introduced into the framework to improve the estimation by providing the best stimulation of the DPS for optimal parameter identification, where trajectories of both sensors and actuators are optimized simultaneously. We also introduce a new methodology to solving fractional-order optimal control problems, with which we demonstrate that we can solve optimal sensing policy problems when sensors move in complex media, displaying fractional dynamics. We consider and solve the problem of optimal scale reconciliation using satellite imagery, ground measurements, and Unmanned Aerial Vehicles (UAV)-based personal remote sensing. Finally, to provide the reader with all the necessary background, the appendices contain important concepts and theorems from the literature as well as the Matlab codes used to numerically solve some of the described problems.

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A minimal covering of a graph G with isomorphic copies of graph H is a set {H1, H2, H3, ... , Hn} where Hi is isomorphic to H, the vertex set of Hi is a subset of G, the edge set of G is a subset of the union of Hi's, and the cardinality of the union of Hi's minus G is minimum. Some studies have been made of covering the complete graph in which case an added condition of the edge set of Hi is the subset of the edge set of G for all i which implies no additional restrictions. However, if G is not the complete graph, then this condition may have implications. We will give necessary and sufficient conditions for minimal coverings of complete bipartite graph with 6-cycles, which we call minimal unrestricted coverings. We also give necessary and sufficient conditions for minimal coverings of the complete bipartite graph with 6-cycles with the added condition the edge set of Hi is a subset of G for all i, and call these minimal restricted coverings.

When approaching a new research problem, we often use screening designs to determine which factors are worth exploring in more detail. Before exploring a problem, we don't know which factors are important. When examining a large number of factors, it is likely that only a handful are significant and that even fewer two-factor interactions will be significant. If there are important interactions, it is likely that they are connected with the handful of significant main effects. Since we don't know beforehand which factors are significant, we want to choose a design that gives us the highest probability a priori of being able to estimate all significant main effects with their associated two-factor interactions. This project examines the methodology of finding designs that do not rely on an assumed model. We propose a method of modifying the D-Optimality criteria that averages over models with a common set of main effects and varying subsets of two-factor interations. We also calculate the proportion of the subsets that produce estimable designs. We use these results to find the best models for given run size and number of main effects.

Within statistical methods, design of experiments (DOE) is well suited to make good inference from a minimal amount of data. Two types of designs within DOE are screening designs and optimization designs. Traditionally, these approaches have been necessarily separated by a gap between the objectives of each design and the methods available. Despite being so separated, in practice these designs are frequently connected by sequential experimentation. In fact, from the genesis of a project, the experimentor often knows that both designs will be necessary to accomplish his objectives. Due to advances in the understanding of experimental designs with complex aliasing and their analysis, a current topic within statistics is how to desegregate these methods into a more unified and economical approach. This project is one treatment of that issue.