一种新的H~∞─优化方法：梯度方法

A GRADIENT APPROACH TO H￣∞-OPTIMIZATION

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：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．

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 ρ(ε, F) is defined,with the relation lim. The differentiability of ρ(ε, F) with 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 . Examples show that the gradient algorithm is very effective in increasing ρ(ε,F). The algorithm converges to stationary points or stops at non-differentiable points.