Research
What is a Hybrid System?
A Hybrid System is a dynamical system composed of discrete state (modes) as well as continuous states. Human beings, for example, can be considered to be Hybrid Systems, since they combine continuous dynamics, such as the movement of arms and legs, with discrete dynamics, such as logical thinking or decision making. Various systems, such as robots, automobiles, aircraft and chemical plants also have continuous elements within their physical dynamics, combined with logical elements in the computer programs.
A Hybrid System can be expressed as in Fig. 1, where the discrete element is given by an automaton and the continuous element is given by a differential equation assigned to each node. The term "mode" in the figure is referred to as the discrete state, and 'x' denotes the continuous state. In the case of a walking robot, there are two modes; two-legged standing mode and single-legged standing mode. The governing equation of motion will switch between these two modes.
Manipulations of an object by a multi-fingered hand would be more complicated. Moreover, the control systems in aircraft and chemical plants consist of various modes, such as the starting mode, the steady mode, the emergency mode, etc..
Research Topics
Until now, controller design for Hybrid Systems has been done by trial and error. However, it will not be easy to design control systems by trial and error in the future, as they will, in general, become very complicated. Thus, since around the 1990's, much attention has been paid to the research topics of Hybrid Systems as a new research domain in the 21st century, both in the field of control engineering and also computer science.
How does a highly functional system like a human being combine continuous dynamics with discrete dynamics? What is a universal principle for designing the optimal system, where the continuous dynamics and the discrete dynamics are intricately combined? Alternatively, is there a principle for individual optimal design? Our laboratory considers such problems and aims to build the theory of intelligent control system design for the next generation, including logical information processing from various points of view.
- Modeling of Systems composed of Logic and Ordinary Differential Equations.
- Development of Simulators for Hybrid Systems.
- Theoretical Analysis of Hybrid Systems.
- Stabilization Problem and Optimal Control Problem of Hybrid Systems.
- Application of Hybrid System Theory to Robots (Walking, Obstacle Avoidance), CPU systems, Automobiles, and Bio systems.