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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