Existence and uniqueness of optimal solutions for multirate partial differential algebraic equations |
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Affiliation: | Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität Greifswald, Walther-Rathenau-Str. 47, D-17489 Greifswald, Germany |
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Abstract: | The numerical simulation of electric circuits including multirate signals can be done by a model based on partial differential algebraic equations. In the case of frequency modulated signals, a local frequency function appears as a degree of freedom in the model. Thus the determination of a solution with a minimum amount of variation is feasible, which allows for resolving on relatively coarse grids. We prove the existence and uniqueness of the optimal solutions in the case of initial-boundary value problems as well as biperiodic boundary value problems. The minimisation problems are also investigated and interpreted in the context of optimal control. Furthermore, we construct a method of characteristics for the computation of optimal solutions in biperiodic problems. Numerical simulations of test examples are presented. |
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Keywords: | Multirate partial differential algebraic equation Optimisation Optimal control Method of characteristics Radio frequency applications |
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