Zonotope bundles for the efficient computation of reachable sets

We introduce zonotope bundles for computing the set of states reachable by a dynamical system, also known as the reachable set. Reachable set computations suffer from the curse of dimensionality, which has been successfully addressed by using zonotopes for linear systems. However, zonotopes are not...

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Bibliographic Details
Published in2011 50th IEEE Conference on Decision and Control and European Control Conference pp. 6814 - 6821
Main Authors Althoff, M., Krogh, B. H.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.2011
Subjects
Complexity theory
Generators
Linear systems
Principal component analysis
Reachability analysis
Vectors
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ISBN9781612848006
1612848001
ISSN0191-2216
DOI10.1109/CDC.2011.6160872

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Summary:We introduce zonotope bundles for computing the set of states reachable by a dynamical system, also known as the reachable set. Reachable set computations suffer from the curse of dimensionality, which has been successfully addressed by using zonotopes for linear systems. However, zonotopes are not closed under intersection leading to challenges when applying them to nonlinear and hybrid problems. We introduce zonotope bundles as the intersection of zonotopes (without explicitly computing the intersection). Zonotope bundles are closed under intersection, while inheriting many positive properties of zonotopes. This is demonstrated for linear, nonlinear, and hybrid systems. A further property of zonotope bundles is that their computation can be easily parallelized.
ISBN:9781612848006
1612848001
ISSN:0191-2216
DOI:10.1109/CDC.2011.6160872