Spatiotemporal Control Without Reference States

当环境发生某些变化时，许多工程设备和生物物理系统会变得不稳定。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由反馈机制控制，这些反馈机制不断监控系统的行为，并将其与所需行为的数学模型进行比较。这里提出的研究解决了当无法获得可靠的数学模型或当系统的某些特性使更传统的控制方法不可能实现时所产生的问题。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的理想参考状态。这项研究应该被视为理解大系统动力学和控制的长期科学努力的一部分，但与当前工程学感兴趣的领域相关的短期结果也是可望的。主要感兴趣的两个例子是半导体激光器，它具有在极快的时间尺度上发生的不稳定性，以及心脏的电活动，这是一个复杂的系统，对其进行足够准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.