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Direct Verification of Linear Systems with over 10000 Dimensions

10 pagesPublished: June 27, 2017

Abstract

We evaluate a recently-proposed reachability method on a set of high-dimensional lin- ear system benchmarks taken from model order reduction and presented in ARCH 2016. The approach uses a state-set representation called a generalized star set and the principle of superposition of linear systems to achieve scalability. The method was previously shown to have promise in terms of scalability for direct analysis of large linear systems. For each benchmark, we also compare computing the basis matrix, a core part of the reachabil- ity method, using numerical simulations versus a matrix exponential formulation. The approach successfully analyzes systems with hundreds of dimensions in minutes, and can scale to systems that have over 10000 dimensions with a computation time ranging from tens of minutes to tens of hours, depending on the desired time step.

Keyphrases: Affine systems, continuous systems, hybrid systems, linear systems, reachability analysis, verification

In: Goran Frehse and Matthias Althoff (editors). ARCH17. 4th International Workshop on Applied Verification of Continuous and Hybrid Systems, vol 48, pages 114--123

Links:
BibTeX entry
@inproceedings{ARCH17:Direct_Verification_of_Linear,
  author    = {Stanley Bak and Parasara Sridhar Duggirala},
  title     = {Direct Verification of Linear Systems with over 10000 Dimensions},
  booktitle = {ARCH17. 4th International Workshop on Applied Verification of Continuous and Hybrid Systems},
  editor    = {Goran Frehse and Matthias Althoff},
  series    = {EPiC Series in Computing},
  volume    = {48},
  pages     = {114--123},
  year      = {2017},
  publisher = {EasyChair},
  bibsource = {EasyChair, http://www.easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/bDRk},
  doi       = {10.29007/dwj1}}
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