University of Twente Student Theses
Decomposed reachability analysis for discrete linear systems
Schipper, M.A. (2019) Decomposed reachability analysis for discrete linear systems.
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| Abstract: | This thesis presents a reachability analysis method using decomposition by projection. A Cartesian product is used for the definition of sub dimensions, which is why conventional independence uses the Cartesian product as a basis. A projection to the subsystems is sufficient for this affect, which means there is a set representation in the system dimension that is propagated. The propagation consists of three steps, the first step is a projection to the sub dimensions. The second step uses the Cartesian product to create a set in the system dimension, which is propagated during the third step. The result of this work is formalized by rewriting matrix multiplication from linear transformations in combination with the symbolic behavior of Zonotope representation. The decomposition by projection results in a method with a tighter flow pipe construction. The first step is an explicit over approximation, which allows for the quantification of over approximation and storage/computational complexity. Last, the method is applied to Jordan decomposition as a generalization of diagonalisation, where a Jordan block is defined as a generalized eigenvalue. This work shows that such a Jordan block is a suitable candidate for decomposition, which is not limited to decomposition by independence. |
| Item Type: | Essay (Master) |
| Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |
| Subject: | 54 computer science |
| Programme: | Embedded Systems MSc (60331) |
| Link to this item: | https://purl.utwente.nl/essays/80354 |
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