Order-Reduction Abstractions for Safety Verification of High-Dimensional Linear Systems
Abstract
Order-reduction is a standard automated approximation technique for computer-aided design, analysis, and simulation of many classes of systems, from circuits to buildings. For a given system, these methods produce a reduced-order system where the dimension of the state-space is smaller, while attempting to preserve behaviors similar to those of the full-order original system. To be used as a sound abstraction for formal verification, a measure of the similarity of behavior must be formalized and computed, which we develop in a computational way for a class of linear systems and periodically-switched systems as the main contributions of this paper. We have implemented the order-reduction as a sound abstraction process through a source-to-source model transformation in the HyST tool and use SpaceEx to compute sets of reachable states to verify properties of the full-order system through analysis of the reduced-order system. Our experimental results suggest systems with on the order of a thousand state variables can be reduced to systems with tens of state variables such that the order-reduction overapproximation error is small enough to prove or disprove safety properties of interest using current reachability analysis tools. Our results illustrate this approach is effective to alleviate the state-space explosion problem for verification of high-dimensional linear systems.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2016
- DOI:
- 10.48550/arXiv.1602.06417
- arXiv:
- arXiv:1602.06417
- Bibcode:
- 2016arXiv160206417T
- Keywords:
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- Computer Science - Systems and Control
- E-Print:
- Preliminary version under review for Discrete Event Dynamic Systems