The method for stabilizing an unstable periodic orbit using time-delayed feedback was proposed by Pyragas. This method is regarded to be of great potential use in a number of contexts, including physical systems, biological systems and machines.
The strongest merit of this method lies in the fact that the orbit that it stabilizes is an existing unstable periodic orbit. In this sense, this method is non-destructive, and for this reason, the energy expended to maintain the state in its stable form is believed to be minimal.
In our research group, we are investigating the application of the feedback method to systems that possess certain kinds of physical symmetries, such as magnetic materials and dielectric materials. This research involves problems of control theory, problems peculiar to physics and problems in statistical mechanics. At this time, there are many unsolved problems that must be addressed.
We plan to begin by studying a greatly simplified model and then gradually work toward the investigation of increasingly realistic systems.
|Assistant Professor Hiroki Tutu|