Feedback Synthesis for Infinite Dimensional Systems Dominated by Nonlinearities

该建议概述了一个全面的计划，在一个新兴领域的控制非线性分布参数系统。 激励性的实际问题来自于不稳定流体流动的稳定，这在当今的先进消费品以及汽车、航空航天和船舶车辆中无处不在。 这些应用程序充满了超线性增长的非线性和不稳定性的空间域的内部控制只能从边界。 这些问题已经成功地处理在有限维的设置，并且是唯一的定位，以解决他们的分布参数systems.This建议提倡两种类型的方法的发展。 首先，基于反推的方法，该方法采用空间域内部的状态测量或非线性观测器，用于具有边界控制的高度不稳定系统的稳定。 控制作用通常通过存在于许多离散参数系统中的粘性/扩散机制从边界传播到域的内部。第二种方法基于仅涉及边界测量的简单反馈。 这样的反馈是在Jurdjevic-Quinn反馈法的形式，增加阻尼的渐近稳定系统与已知的控制李雅普诺夫函数。 一个例子示出的流体流动的问题，其中的J-Q型控制器的开发低雷诺数，并证明其有效性的高，现实的雷诺数值，许多数量级高于设计值。 在同样的情况下，该建议提出超越平衡稳定化，以实施非平衡准定常运动。 这种控制目标的一个例子是在流体中混合，其中人们希望通过确定性手段实现颗粒的随机运动。 该建议计划大大偏离传统的方法，这个问题都是开环/运动规划类型。 一个反馈定律将被证明，提高了湍流动能和涡量的流体在不确定非线性系统的镇定问题上，已经取得了一些理论上的进展（获得了几个最佳论文奖和一本关于这个主题的新书），以及过渡（我们的控制算法的工业实验和一项专利提供给一家领先的航空发动机制造商进行许可考虑。

This proposal outlines a comprehensive program in an emerging area of control of nonlinear distributed parameter systems. The motivating practical problems come from stabilization of unstable fluid flows, ubiquitous in today's advanced consumer products and automotive, aerospace, and marine vehicles. These applications abound with nonlinearities of superlinear growth and instabilities in the interior of a spatial domain where controls can act only from the boundary. These issues have successfully been dealt with in a finite-dimensional setting, and are uniquely positioned to address them for distributed parameter systems.This proposal advocates the development of two types of methods. First, methods based on backstepping, which employ either the measurement of the state in the interior of the spatial domain, or a nonlinear observer, for stabilization of highly unstable systems with boundary controls. The control action is typically propageted from the boundary into the interior of the domain by viscosity/diffusion mechanisms present in many disstributed parameter systems.The second method is based on simple feedbacks involving only boundary measurements. Such feedbacks are in the form of Jurdjevic-Quinn feedback laws that add damping for asymptotic stabilization of systems with known control Lyapunov functions. An example is shown of a fluid flow problem in which a J-Q type controller is developed for low Reynolds number and demonstrate its effectiveness for a high, realistic value of Reynolds number, many orders of magnitude higher than the design value. In the same setting, this proposal proposes to go beyond equilibrium stablization, to enforcement of non-equilibrium quasi-steady motion. An example of such a control objective is mixing in fluids where one wants to achieve random motion of particles by deterministic means. This proposal plans to dramatically depart from conventional approaches to this problem which are all of open-loop/motion-planning type. A feedback law will be shown that raises both the turbulent kinetic energy and the vorticity of the fluid (uniformly in space).Several theoretical advances have been produced in stabilization of uncertain nonlinear systems (resulting in several best paper awards and a new book on this topic), as well as transition (industrial experiments with our control algorithms and a patent offered for licensing consideration to a leading aeroengine manufacturer.