Splitting algorithms and circuit analysis

TL;DR

This paper introduces specialized splitting algorithms for analyzing complex electrical circuits and systems modeled by monotone and anti-monotone relations, improving solution methods for nested sum and inverse structures.

Contribution

It presents new splitting algorithms tailored to the structure of series and parallel circuit interconnections involving monotone and anti-monotone relations.

Findings

Algorithms effectively handle nested sums and inverses in circuit models

Enhanced convergence properties for complex interconnection structures

Applicable to a wide range of electrical and control systems

Abstract

The splitting algorithms of monotone operator theory find zeros of sums of relations. This corresponds to solving series or parallel one-port electrical circuits, or the negative feedback interconnection of two subsystems. One-port circuits with series and parallel interconnections, or block diagrams with multiple forward and return paths, give rise to current-voltage relations consisting of nested sums and inverses. In this extended abstract, we present new splitting algorithms specially suited to these structures, for interconnections of monotone and anti-monotone relations.