基于比例关系图的电路模型简化
Circuit Model Reduction with Scaled Relative Graphs
摘要：
连分数是复杂对象（例如实数）作为简单对象（例如整数）的和与逆的经典表示。线性电路理论中的类比是串联/并联单端口链：端口行为是包含其元件的端口行为的连分数。截断连分数是一种经典的近似方法，相当于删除离端口最远的电路元件。我们将这个想法应用到链的串联/并联单端口组成的任意非线性关系。这给出了一种模型简化方法，该方法自动保留诸如增量正性的属性。Scaled Relative Graph（SRG）给出了原始和截断端口行为的图形表示。这些SRG的差异给出了一个界的近似误差，这是具有竞争力的现有方法。
英文摘要：
Continued fractions are classical representations of complex objects (for example, real numbers) as sums and inverses of simpler objects (for example, integers). The analogy in linear circuit theory is a chain of series/parallel one-ports: the port behavior is a continued fraction containing the port behaviors of its elements. Truncating a continued fraction is a classical method of approximation, which corresponds to deleting the circuit elements furthest from the port. We apply this idea to chains of series/parallel one-ports composed of arbitrary nonlinear relations. This gives a model reduction method which automatically preserves properties such as incremental positivity. The Scaled Relative Graph (SRG) gives a graphical representation of the original and truncated port behaviors. The difference of these SRGs gives a bound on the approximation error, which is shown to be competitive with existing methods.
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