# Research

## System Control

A “system” is a mathematical representation of an object with inputs and outputs. The methodology for analyzing and designing systems, especially those with dynamics is referred to as “system control.” In this laboratory, we focus on constructing theories of system control applicable not only to aerospace but also to various systems including mechanical, electrical, physical, chemical, informational, and social systems.

Our research includes main themes such as nonlinear control, optimal control, probabilistic system control, robotics, and machine learning, among others. Developing these theories necessitates the integration of knowledge from multiple disciplines, particularly linear algebra, differential geometry, functional analysis, analytical mechanics, aerospace dynamics, probability statistics, statistical learning, mechatronics, and computer science.

In recent years, our emphasis has been on developing topics like nonlinear control based on analytical mechanics principles for mechanical systems and nonlinear optimal control using databases.

## System Identification

In the control of systems, mathematical models that represent the dynamics of the target system are crucial. The accuracy of the mathematical model strongly influences the performance and safety of the designed controllers. However, it is challenging to construct mathematical models for systems with complex dynamics. Therefore, a systematic approach to model construction based on large amounts of input/output data, known as “system identification,” is essential.

We are developing system identification methods that utilize machine learning to construct mathematical models for systems with significant nonlinearity. Additionally, our laboratory is currently developing control theories that utilize the models identified through this process.

## Aerospace Systems

Aircraft and spacecraft systems require highly precise and reliable control. In aviation, there is a requirement for multifunctional controls capable of managing complex models (e.g., fluid dynamics), and large-scale systems (e.g., air traffic control). For space missions, achieving a balance between fuel efficiency and high-precision control is essential, especially under the extreme conditions of outer space.

In our laboratory, we focus on developing effective strategies for aerospace system control. Our research includes fuel-efficient control through trajectory planning using nonlinear optimization methods like sparse optimization. We also create control methods for spacecraft, such as attitude control and rendezvous operations, by leveraging the dynamical properties of the spacecraft. These methodologies are applied to address various challenges in both aeronautics and astronautics.