Baar, W. (2015) Model reduction of consensus networks. Bachelor's Thesis, Mathematics.
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Abstract
In this thesis, model reduction of consensus networks is studied. A network can be algebraically represented by a graph and we study its edge Laplacian. We consider a network which contains one cycle. We compare that system with the system described by only its underlying spanning tree, and we derive an exact H2-norm of the error system. This error term depends on the eigenvalues and orthonormal eigenvectors of the edge Laplacian and the position and length of the cycle. If we consider a star graph as spanning tree the error is constant, that is, independent of the number of nodes (agents). We derive numerical results for the H2-norm for systems where the spanning tree is a path graph.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 15 Feb 2018 08:06 |
| Last Modified: | 15 Feb 2018 08:06 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/13094 |
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