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DAE‐formulation for optimal solutions of a multirate model
Author(s) -
Pulch Roland,
Kugelmann Bernd
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510297
Subject(s) - discretization , mathematics , algebraic number , algebraic equation , boundary value problem , differential algebraic equation , ring (chemistry) , differential (mechanical device) , partial differential equation , differential equation , method of lines , control theory (sociology) , mathematical analysis , ordinary differential equation , computer science , physics , nonlinear system , chemistry , control (management) , organic chemistry , artificial intelligence , quantum mechanics , thermodynamics
A dynamical system including frequency modulated signals can be transformed into multirate partial differential algebraic equations. Optimal solutions are determined by a necessary condition. A method of lines yields a semi‐discretisation in the case of initial‐boundary value problems. We show that the resulting system can be written in a standard formulation of differential algebraic equations. Hence appropriate time integration schemes are available for a numerical solution. We present results for a test example modelling the electric circuit of a ring oscillator. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)