Control of Patterns in Systems With Large Numbers of Actuators and Sensors

随着微机电系统的出现，我们正在快速接近必须了解如何控制包含大量执行器和传感器的非线性系统的日子。下一代应用，如全息数据存储设备和波分复用，将需要新的精密模拟控制方法。与此同时，科学家们才刚刚开始瞥见高等动物大脑中的信息处理活动。有人认为，理解控制理论方面的模式生成在大规模的致动器/传感器阵列是成功地解决这些具有挑战性的技术问题的核心。感兴趣的代表性模式将是孤立波、定常脉冲、行波和螺旋波。现有的理论解释了这些模式的稳定性，但未能解决如何控制它们。一项研究计划的重点是控制这些模式在可取的方式概述的建议。主要的数学工具将是（a）对称网络中的波生成，（B）孤子理论，（c）螺旋波，和（d）激励器-抑制器方程。有人认为，在每种情况下概述的反馈控制技术可以推进国家的最先进的显着，通过讨论潜在的应用在微机电系统阵列的控制，了解原始动物的大脑的信号处理方面，并作为模板模型的尖峰网络。

With the emergence of micro electromechanical systems, we are fast approaching the days of having to understand how to control nonlinear systems containing massive numbers of actuators and sensors. Next generation applications such as holographic data storage devices, and wavelength division multiplexing, will require novel precision analog control methodology. At the same time, scientists are only beginning to get a glimpse of information processing activities in the brains of higher animals. It is argued that understanding control theoretic aspects of pattern generation in massive actuator/sensor arrays is central to successfully tackling these challenging technological problems. Representative patterns of interest will be solitary waves, stationary impulses, travelling waves, and spiral waves. Existing theories explain the stability of these patterns, but fail to address how to control them. A research program focussingon controlling these patterns in desirable ways is outlined in the proposal. Primary mathematical tools will be (a) wave generation in networks with symmetry, (b) theory of solitons, (c) spiral waves, and (d) actuator-inhibitor equations. It is argued that feedback control techniques outlined in each case can advance the state-of art significantly, by discussing potential applications in the control of arrays of micro electromechanical systems, understanding signal processing aspects of the brain of primitive animals, and as template models of spiking networks.