Many engineered devices and biophysical systems become unstable when subjected to certain changes in their environments. Such instabilities can result in a substantial loss of efficiency, or in catastrophic failure. These instabilities can sometimes be controlled by feedback mechanisms that constantly monitor the system's behavior and compare it to a mathematical model of the desired behavior. The research proposed here addresses issues that arise when faithful mathematical models are unavailable or when some characteristic of the system makes it impossible to implement more conventional control methods. The research will focus on the use of time-delay methods that substitute the past behavior of the system itself for the computed ideal reference state. This research should be viewed as part of a long-term scientific effort to understand the dynamics and control of large systems, but short-term results relevant to areas of current engineering interest are expected as well. Two examples of primary interest are semiconductor lasers, which have instabilities that occur on extremely fast time scales, and electrical activity in the heart, a complex system for which sufficiently accurate mathematical modeling is extremely difficult.
