论文标题
稳定正网络系统的模型重建方法还原
Reduced model reconstruction method for stable positive network systems
论文作者
论文摘要
我们考虑了减少稳定的正网络系统的重建问题，并基于$ H^2 $最佳模型减少问题的原始互连结构的保存。为此，我们使用非负矩阵的perron--frobenius理论来定义一个重要的集合，使得集合的所有元素都是稳定且均具有元元素。在集合上使用投影，我们提出了一种环状投影梯度方法，以比初始减少模型在$ h^2 $ norm的意义上产生更好的模型。在该方法中，我们使用目标函数梯度的Lipschitz常数来定义步骤大小，而无需线搜索方法，其计算复杂性很大。此外，Lipschitz常数的存在确保了我们提议的算法与固定点的全球融合。 数值实验表明，所提出的算法改善了给定的减少模型，可用于大规模系统。
We consider a reconstruction problem of a reduced stable positive network system with the preservation of the original interconnection structure based on an $H^2$ optimal model reduction problem with constraints. To this end, we define an important set using the Perron--Frobenius theory of nonnegative matrices such that all elements of the set are stable and Metzler. Using the projection onto the set, we propose a cyclic projected gradient method to produce a better reduced model than an initial reduced model in the sense of the $H^2$ norm. In the method, we use Lipschitz constants of the gradients of our objective function to define the step sizes without a line search method whose computational complexity is large. Moreover, the existence of the Lipschitz constants guarantees the global convergence of our proposed algorithm to a stationary point. The numerical experiments demonstrate that the proposed algorithm improves a given reduced model, and can be used for large-scale systems.
