优化H-范数的新技术与鲁棒设计

A New Approach to Optimize the H- Norm and Robust Design

中文关键词  H-范数  梯度方法  Hamilton矩阵  特征轨迹  结构式不确定性

英文关键词  H- norm  the gradient method  Hamilton matrix  eigenvalue loci  structured uncertainty

中文摘要

      本文提出了一种全新的H-优化方法：梯度方法。这种优化方法非常灵活，适用范围极广，可用于对系统矩阵中的一般参数进行优化选择，可将H-范数与其他范数加权，构成复合的目标函数，还可处理极点配置等限制条件下的H-优化问题。梯度方法的主要思想就是通过与H-范数直接相关的Hamilton矩阵定义目标函数p(e,p), 具有limp(e,p)=1/∥T(s,p)∥-.其中p可为系统矩阵中的任何可变参数。p(e,p)对p的导数可以求出，因而可用梯度方法极大化p(e,p)，从而极小化∥T(s,p)∥-.本文用此方法对结构式不确定系统进行鲁棒设计，并带有极点配置的约束。实例显示，梯度方法的效果很好。

英文摘要

      This paper will provide a gradient method for H- optimization. This new method can be flexibly used for a wide range of design objectives. For example, it can be used to optimize an H- norm under the constraint of pole assignment. The main idea of the gradient method is to define an objective function p(e,p) through a Hamilton matrix that is closely related to the H- norm, with the relation that limp(e,p)=1/∥T(s,p)∥-, in which p can be any parameter in the system matrices. The differential dp(e,p) / dp is derived in the paper, so p(e,p) can be maximized by gradient method, thus ∥T(s,p)∥- is minimized. This method is utilized for robust design of system with structured uncertainty under the constraint of pole assignment. Example show that the method is very effective.