Hybrid systems of differential-algebraic equations - Analysis and numerical solution
Please always quote using this URN:urn:nbn:de:0296-matheon-5362
- We consider hybrid systems of differential-algebraic equations and present a general framework for general nonlinear over- and underdetermined hybrid systems that allows the analysis of existence and uniqueness and the application of index reduction methods for hybrid differential-algebraic systems. A particular difficulty in the numerical simulation of hybrid systems is (numerical) chattering, i.e., fast oscillations between modes of operations. A regularization technique using sliding modes allows to regularize the system behavior in the case of chattering. Further, we show how chattering behavior during the numerical solution can be prevented using sliding mode simulation. The advantage of the sliding mode simulation is illustrated by numerical examples.
Author: | Volker Mehrmann, Lena Scholz |
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URN: | urn:nbn:de:0296-matheon-5362 |
Referee: | Peter Deuflhard |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2008/08/12 |
Release Date: | 2008/08/12 |
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Institute: | Technische Universität Berlin |
MSC-Classification: | 34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Axx General theory / 34A09 Implicit equations, differential-algebraic equations [See also 65L80] |
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Axx General theory / 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions | |
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L05 Initial value problems | |
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L80 Methods for differential-algebraic equations | |
Preprint Number: | 531 |