EFFICIENT COMPUTER ALGORITHMS FOR PIECEWISE-LINEAR ANALYSIS OF RESISTIVE NONLINEAR NETWORKS
EFFICIENT COMPUTER ALGORITHMS FOR PIECEWISE-LINEAR ANALYSIS OF RESISTIVE NONLINEAR NETWORKS
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DOI：
10.1109/tct.1971.1083219
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发表时间：
1971-01-01
期刊：
影响因子：
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通讯作者：
CHUA, LO
中科院分区：
文献类型：
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作者：
CHUA, LO
本文提出了两种求解含两端线性和非线性电阻、独立直流电压源和电流源以及线性受控源的阻性非线性网络直流解的有效计算机算法。第一种算法是专门为具有多个解的网络设计的，而第二种算法是为具有唯一解的网络设计的。第一种算法基于与网络的线性n端口部分相关联的混合参数的符号。第二种算法是牛顿-拉夫逊方法的分段线性版本，但它在两个重要方面不同于可微版本。首先，分段线性算法的发散现象不是像通常情况下那样发散，而是采取两个或更多个段组合的循环重复的形式。其次，迭代公式不直接依赖于前一次迭代的解，而是依赖于更新后的线段组合。这些观察导致一个算法，确保分段线性版本的牛顿-拉夫森公式将始终收敛。此外，在第二种算法的迭代公式与第一种算法的网络方程相同的基础上，建立了两种算法之间的重要联系。
Two efficient computer algorithms are presented for finding the dc solutions of resistive nonlinear networks containing two-terminal linear and nonlinear resistors, independent dc voltage and current sources, and linear controlled sources. The first algorithm is designed specifically for networks with multiple solutions, while the second algorithm is designed for networks with a unique solution. The first algorithm is based on the sign of the hybrid parameters associated with the linear n-port portion of the network. The second algorithm is a piecewise-linear version of the Newton-Raphson method, but it differs from the differentiable version in two important aspects. First, rather than diverging to, as in the usual case, the divergence phenomenon of the piecewise-linear algorithm takes the form of a cyclic repetition of two or more segment combinations. Second, the iteration formula depends not directly on the solution at the preceding iteration, but on the updated segment combination. These observations lead to an algorithm which assures that the piecewise-linear version of Newton-Raphson formula will always converge. Moreover, an important connection between the two algorithms is established on the basis that the iteration formula for the second algorithm is identical to the network equations associated with the first algorithm.