一种新的H∞-优化方法:梯度方法
A Gradient Approach to H∞-Optimization
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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.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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Key words:
- H∞-norm /
- gradient method /
- differentiability /
- pole assignment
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