NDLI: Analysis of nonlinear electrical circuits using bernstein polynomials

Content Provider	Springer Nature Link
Author	Arounassalame, M.
Copyright Year	2012
Abstract	In electrical circuit analysis, it is often necessary to find the set of all direct current (d.c.) operating points (either voltages or currents) of nonlinear circuits. In general, these nonlinear equations are often represented as polynomial systems. In this paper, we address the problem of finding the solutions of nonlinear electrical circuits, which are modeled as systems of n polynomial equations contained in an n-dimensional box. Branch and Bound algorithms based on interval methods can give guaranteed enclosures for the solution. However, because of repeated evaluations of the function values, these methods tend to become slower. Branch and Bound algorithm based on Bernstein coefficients can be used to solve the systems of polynomial equations. This avoids the repeated evaluation of function values, but maintains more or less the same number of iterations as that of interval branch and bound methods. We propose an algorithm for obtaining the solution of polynomial systems, which includes a pruning step using Bernstein Krawczyk operator and a Bernstein Coefficient Contraction algorithm to obtain Bernstein coefficients of the new domain. We solved three circuit analysis problems using our proposed algorithm. We compared the performance of our proposed algorithm with INTLAB based solver and found that our proposed algorithm is more efficient and fast.
Starting Page	81
Ending Page	86
Page Count	6
File Format	PDF
ISSN	14768186
Journal	International Journal of Automation and Computing
Volume Number	9
Issue Number	1
e-ISSN	17518520
Language	English
Publisher	Institute of Automation, Chinese Academy of Sciences
Publisher Date	2012-02-22
Publisher Place	Heidelberg
Access Restriction	Subscribed
Subject Keyword	Nonlinear circuit analysis Bernstein polynomials Krawczyk operator interval analysis polynomial system Computer-Aided Engineering (CAD, CAE) and Design Computer Applications Control, Robotics, Mechatronics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Control and Systems Engineering Modeling and Simulation Computer Science Applications

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