PYI: Nonlinear Control and Order Reduction

这项奖项将资助研究开发一种 非线性系统降阶的方法，它（i）尊重 并保持原始模型的非线性，（ii）不 需要各种系统的相对速度的准确知识 变量，以及（iii）包含外生控制的影响 输入. 研究结果对非线性控制器的设计具有指导意义 具有快速和慢速模式的系统设计。 有两大原因 用于开发非线性模型降阶技术。 第一 是所有大型动力工程系统的共同点： 的控制方程。 第二个原因是， 非线性效应不能忽略，因为它们通常是 对许多先进工程的性能具有决定性影响 系统，如高性能飞机，快速机动 航天器和化学反应堆。 只有第一个问题是 考虑在标准技术的第一线性化的动态 方程，然后使用线性模型降阶技术。 显然，任何非线性效应（如分叉，甚至非线性 瞬态响应）将使用该方法丢失。 主要 这项研究的分析框架包括多参数奇异 微扰理论和中心流形理论。 这两个强大 工具将被合并和扩展。泛函分析结果的应用 如所谓的硬隐函数定理。 的 保华奖资助的研究项目涉及 非线性系统模型降阶方法的发展 系统. 该方法将试图保持非线性的性质， 因为非线性可能是决定 影响了许多先进的工程系统。

This PYI award will fund research into the development of a methodology for order reduction of nonlinear systems which (i) respects and preserves the nonlinearity of the original model, (ii) does not require exact knowledge of the relative speeds of various system variables, and (iii) incorporates the effect of an exogenous control input. The results will have implications for nonlinear controller design of systems with fast and slow modes. There are two major reasons for developing a nonlinear model order reduction technique. The first is common to all large dynamical engineering systems: the large number of governing equations. The second reason concerns the fact that nonlinear effects can not be neglected since they will often be the deciding influence in the performance of many advanced engineering systems, such as high-performance aircraft, rapidly maneuvering spacecraft, and chemical reactors. Only the first of these issues is considered in the standard technique of first linearizing the dynamical equations and then using a linear model order reduction technique. Clearly, any nonlinear effect (such as bifurcations, or even nonlinear transient response) will be lost using this approach. The main analytical framework for this study consists of multiparameter singular perturbation theory and center manifold theory. These two powerful tools will be merged and extended. Use of functional-analytic results such as the so-called hard implicit function theorem will be made. The research supported under this PYI award concerns the development of a methodology for model order reduction of nonlinear systems. The approach will attempt to preserve the nonlinear nature of the original system since the nonlinearities may be the deciding influence in many advanced engineering systems.