Spatiotemporal Control Without Reference States

许多工程设备和生物物理系统在其环境发生某些变化时变得不稳定。 这种不稳定性可能导致效率的显著损失或灾难性故障。 这些不稳定性有时可以通过反馈机制来控制，反馈机制不断地监控系统的行为，并将其与期望行为的数学模型进行比较。 这里提出的研究解决问题时出现的忠实的数学模型是不可用的，或者当系统的某些特性使得它不可能实现更传统的控制方法。 研究将集中在使用时间延迟的方法，取代过去的行为系统本身的计算理想的参考状态。 这项研究应被视为长期科学努力的一部分，以了解大型系统的动力学和控制，但短期的结果相关的领域，目前的工程利益，以及预期。 主要感兴趣的两个例子是半导体激光器，其具有在极快的时间尺度上发生的不稳定性，以及心脏中的电活动，这是一个非常复杂的系统，非常难以进行足够精确的数学建模。

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.