Feedback Design for Nonlinear Systems

这个数学科学项目的一个主要目标是开发系统设计反馈律的方法，从而能够塑造或至少影响表现出复杂动力学行为的系统的稳态响应。特别是，研究计划的重点是反馈设计方法的问题，渐近跟踪，干扰抑制，和输出调节 非线性分布参数系统 这个数学科学项目的主要目标是开发一种方法， 控制或影响各种物理现象中出现的非线性效应。 这一目标部分是由燃烧控制中的问题激发的，其中非线性效应实际上可以改善混合，因此原则上可以改善例如汽车的发动机性能。的另一示例 在流体流动问题中，非线性控制的潜在影响是在空气动力学应用中对不稳定性的控制方面，这些不稳定性已经在实验上被证明对飞机的失速和升力特性有很大的影响，并且已知这些不稳定性会导致飞机的失速和升力特性的降低 在 飞机寿命周期 零件. 其他应用是各种设备的有源噪声控制，例如压缩机。

A principal objective of this mathematical sciences project is the development of methods for the systematic design of feedback laws leading to the ability to shape, or at least influence, the steady state response of systems exhibiting complex dynamical behavior. In particular, the research program focuses on feedback design methods for problems of asymptotic tracking, disturbance rejection, and output regulation for nonlinear distributed parameter systems. A primary objective of this mathematical sciences project is the development of a methodology to systematically control or influence nonlinear effects which arise in a variety of physical phenomena. This goal is motivated in part by problems in combustion control, where nonlinear effects actually can improve mixing and hence can , in principle, improve the engine performance of automobiles, for example. Another example of the potential impact of nonlinear control in flluid flow problems is in the control of instabilities in aerodynamic applications, which have been experimentally shown to greatly influence stall and lift behavior of aircraft and which are known to lead to reduction in the life cycle of aircraft parts. Other applications are to active noise control of various devises, such as compressors.