Spatiotemporal Control Without Reference States

许多工程装置和生物物理系统在其环境受到某些变化时变得不稳定。这种不稳定性可能会导致效率的大幅下降，或者导致灾难性的故障。这些不稳定性有时可以通过不断监控系统行为的反馈机制来控制，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了当可靠的数学模型不可用或当系统的某些特性使得无法实现更传统的控制方法时出现的问题。研究将集中在使用时滞方法，用系统本身的过去行为代替计算出的理想参考状态。这项研究应该被视为理解大型系统的动力学和控制的长期科学努力的一部分，但是与当前工程兴趣领域相关的短期结果也被期望。主要关注的两个例子是半导体激光器，它在极快的时间尺度上具有不稳定性，以及心脏中的电活动，这是一个复杂的系统，对其进行足够精确的数学建模是极其困难的。

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.