| 一种新的H∞-优化方法:梯度方法 |
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| 引用本文： | 胡庭姝,陈力.一种新的H∞-优化方法:梯度方法[J].自动化学报,1996,22(2):145-153. |
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| 作者姓名： | 胡庭姝 陈力 |
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| 作者单位： | 1.上海交通大学自动化系 |
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| 摘 要： | 提出一种灵活、有效的H∞-优化方法:梯度方法.利用H∞-范数与状态空间实现的关系,
定义了目标函数ρ(ε,F),ρ(ε,F)与H∞-范数之间的关系是:
limρ(ε,F)=1/‖T(s,F)‖∞
ε→0
分析了ρ(ε,F)的可微性,并给出了ρ(ε,F)/F的具体表达式以及使ρ(ε,F)极大化的梯
度方法,从而导致‖T(s,F)‖∞的极小化.实例表明,梯度方法能有效地使ρ(ε,F)上升,并
收敛于驻点或终止于不可微点.
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| 关 键 词： | H∞-范数 梯度方法 可微性 极点配置 |
| 收稿时间： | 1993-8-23 |
A Gradient Approach to H∞-Optimization |
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| Hu Tingsu,Chen Li.A Gradient Approach to H∞-Optimization[J].Acta Automatica Sinica,1996,22(2):145-153. |
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| Authors: | Hu Tingsu Chen Li |
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| Affiliation: | 1.Dept.of Autonatic Control,Shanghai Jiaotong Univ.Shanghai |
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| Abstract: | In this paper, a gradient approach to H∞-optimization is presented. This new
approach is very effective and flexible. Through the relation between the H~-norm
and state-space representation, an alternative performance index p(ε,F) is defined,
with the relation limρ(ε,F)=‖T(s,F)‖-1∞ The differentiability of ρ(ε,F) with
ε→0
respect to F is investigated and ρ(ε,F)/F is provided. A gradient algorithm is
derived to maximize ρ(ε,F), and hence to minimize ‖T(ε,F)‖∞φ. Examples show
that the gradient algorithm is very effective in increasing o(ε,F). The algorithm
converges to stationary points or stops at non-differentiable points. |
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| Keywords: | H∞-norm gradient method differentiability pole assignment |
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