A Practical Approach to Nonlinear Robust Control

非线性鲁棒控制的实用方法

• 批准号: 9732917
• 负责人: Randal Beard
• 金额: $ 15.52万
• 依托单位: Brigham Young University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-09-01 至 2002-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9732917&HistoricalAwards=false
• 关键词: Practical; Approach; Nonlinear; Robust; Control

9732917BeardLinear H-infinity control is a technique for designing control laws that are robust with respect to bounded variations in system parameters and bounded external disturbances. In recent years, linear H-infinity techniques have been extended to nonlinear system. The nonlinear H-infinity control problem is solved by two first order nonlinear partial differential equations called Hamilton-Jacobi-Isaacs equations. These equations are extremely difficult to solve except in very special cases and they are difficult to approximate by standard techniques except for low order systems. The inability to solve these equations has lead to a failure to realize the potential of nonlinear H-infinity control techniques.This proposal outlines a plan to investigate innovative and computationally practical techniques for approximating closed-loop nonlinear H-infinity optimal control laws. The approach is to approximate the Hamilton-Jacobi-Isaacs equation in a two step procedure. First, an iteration in policy space is used to reduce the nonlinear partial differential equation to an infinite sequence of linear partial differential equations. The second step uses the Galerkin spectral method to approximate each linear partial differential equation. The result of this process is a feedback control law, with a well defined region of attraction, that converges to the nonlinear H-infinity solution as the order of approximation increases. The two step process outlined above suffers from Bellman's "curse of dimensionality," i.e., the required computations and memory increase exponentially with the order of the system. This "curse of dimensionality" is overcome by exploiting the structure in the problem for a fairly general class of nonlinear systems.The proposed research will advance the state of the art by supplying a practical method for approximating nonlinear H-infinity control laws. This result will be helpful to researchers working in the area, allowing them to test their ideas on real world problems, and to practicing engineers who wish to implement the latest developments in control theory research. The proposed research also advances the state of knowledge by illustrating how to mitigate the "curse of dimensionality" by exploiting the structure of optimal control for a certain class of nonlinear systems. ***

9732917Beardlinear H-infinity控制是一种设计控制定律的技术，该技术相对于系统参数和有限的外部干扰的有限变化具有牢固的变化。 近年来，线性h-赋值技术已扩展到非线性系统。 非线性H-赋值控制问题通过称为Hamilton-Jacobi-ISAACS方程的两个一阶非线性偏微分方程解决。 除了在非常特殊的情况下，这些方程式难以解决，并且除了低订单系统外，它们难以通过标准技术近似。 无法求解这些方程式已经导致未能实现非线性H-赋值控制技术的潜力。该提案概述了一项计划，以调查用于近似闭环的非线性Hi-Infinity Hi-Infinity Hifinity Hi-Infinity最佳控制法律的创新和计算实用技术。 该方法是在两步过程中近似汉密尔顿 - 雅各布-ISAACS方程。 首先，策略空间中的迭代用于将非线性偏微分方程减少为线性偏微分方程的无限序列。 第二步使用Galerkin光谱法来近似每个线性偏微分方程。 该过程的结果是一个反馈控制定律，具有明确的吸引力区域，随着近似值的增加，它会收敛到非线性H-触发溶液。 上面概述的两个步骤过程遭受了Bellman的“维​​度诅咒”，即所需的计算和内存随系统的顺序成倍增加。 通过利用问题中相当一般的非线性系统类别中的结构来克服这种“维度的诅咒”。拟议的研究将通过提供近似非线性H-智力控制法的实用方法来提高最新技术状态。 该结果将对在该地区工作的研究人员有所帮助，使他们能够测试他们对现实世界问题的想法，并实践希望实施控制理论研究中最新发展的工程师。 拟议的研究还通过说明如何通过利用特定类别非线性系统的最佳控制结构来减轻知识的状态来推动知识的状态。 ***