Control Systems Theory with Algebraic Techniques and Symbolic Computation

Most things in modern society, such as refrigerators, air conditioners, and even artificial satellites during their space travels, are controlled by using advanced technologies based on control systems theory. The notion of feedback is one of the most important ideas in control systems theory. Feedback control is a way to operate a system as we want by repeating two processes rapidly: observing the state of the system and applying the control input computed from the observation to the system. In recent years, as the required performance and the system dynamics have become more sophisticated, this feedback control loop has become difficult to be performed rapidly enough. To realize the feedback control of such complicated systems with enough performance, I utilize symbolic computation based on mathematical techniques from Abstract Algebra. Roughly speaking, Algebra is a field of mathematics on the rules of calculations. By virtue of the techniques from Algebra, we can compute not only numerics but also mathematical symbolic expressions such as equations or functions themselves, which is called symbolic computation. Symbolic computation can be used to decompose and simplify a feedback control problem before the controlled system is started to operate. This leads to the reduction of the computational cost for the feedback control of the system. As another topic, I'm interested in how control systems theory looks from the abstract and overlooking perspective of Algebra.

• 2018 Research Fellow (DC1), Japan Society for the Promotion of Science
• 2021 Ph. D. (Informatics) Kyoto University
• 2021 Assistant Professor, Graduate School of Information Science and Technology, Osaka University