Splitting algorithms and circuit analysis

2022/08/09 by Chaffey, Thomas, Das, Amritam, Sepulchre, Rodolphe
#47H05 #47N70 #93C10 #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2208.04765

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.

Related

• An approximate analytical (structural) superposition in terms of two, or more, "alfa"-circuits of the same topology: Pt. 2 - the "internal circuit mechanism"
• Monotone RLC Circuits
• Circuit realization and hardware linearization of monotone operator equilibrium networks
• Props in Network Theory
• Superposition principle in linear networks with controlled sources