Collaboration and Application of the theory of multi-agent system, hypergraph, and optimal control

Reference No.	2025a030
Type/Category	Grant for General Research-Workshop（Ⅱ）
Title of Research Project	Collaboration and Application of the theory of multi-agent system, hypergraph, and optimal control
Principal Investigator	Shun UCHIDA（Oita University, Faculty of Science and Engineering・Lecturer）
Research Period	August 22,2025. - August 22,2025.
Keyword(s) of Research Fields	multi-agent system, hypergraph, optimal control theory, nonlinear evolution equation
Abstract for Research Report	The multi-agent system is composed of several members cooperating to achieve a certain goal through the interaction on a network with each other. The multi-agent system has a wide range of applications, e.g., the control of drones and the communication in sensor networks. On the other hand, the hypergraph is a generalization of the discrete graph and is composed of groups of multiple elements such as the communities on social media or the relations of co-authorship. Last year, we were adopted for the Grant for Project Research of Kyushu University (Workshop (Ⅱ)). In this workshop, we discussed the possibility of extending the network of a multi-agent system to a hypergraph and the applications of the theory of optimal control to the multi-agent system. Based on this background, this symposium aims to invite researchers specializing in multi-agent systems, hypergraphs, and optimal control theory in order to exchange information on the latest results and concerns in each field, and to consider mathematical problems from a new perspective. The network in a multi-agent system is usually described by a usual graph in which two points are connected by line segments. By generalizing this theory to a hypergraph, we might be able to apply the concept of a multi-agent system to more complex network structures and to develop into a wider range of models. We can also expect to set a new mathematical problem and obtain its solutions from the perspective of the optimal control theory on hypergraphs. Furthermore, by mutually understanding the concerns of various fields, we can expect cooperation between each field and the emergence of new mathematical theories.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Shun UCHIDA（Oita University・Lecturer） Takeshi FUKAO（Ryukoku University・Professor） Masahiro Ikeda（RIKEN/Keio University・Researcher/Visiting Researcher）