Invariant, Viability and Discriminating Kernel Under-Approximation via Zonotope Scaling
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| author | Mitchell, Ian M. Budzis, Jacob Bolyachevets, Andriy |
| author_facet | Mitchell, Ian M. Budzis, Jacob Bolyachevets, Andriy |
| contents | Scalable safety verification of continuous state dynamic systems has been demonstrated through both reachability and viability analyses using parametric set representations; however, these two analyses are not interchangable in practice for such parametric representations. In this paper we consider viability analysis for discrete time affine dynamic systems with adversarial inputs. Given a set of state and input constraints, and treating the inputs in best-case and/or worst-case fashion, we construct invariant, viable and discriminating sets, which must therefore under-approximate the invariant, viable and discriminating kernels respectively. The sets are constructed by scaling zonotopes represented in center-generator form. The scale factors are found through efficient convex optimizations. The results are demonstrated on two toy examples and a six dimensional nonlinear longitudinal model of a quadrotor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_01006 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Invariant, Viability and Discriminating Kernel Under-Approximation via Zonotope Scaling Mitchell, Ian M. Budzis, Jacob Bolyachevets, Andriy Systems and Control Optimization and Control Scalable safety verification of continuous state dynamic systems has been demonstrated through both reachability and viability analyses using parametric set representations; however, these two analyses are not interchangable in practice for such parametric representations. In this paper we consider viability analysis for discrete time affine dynamic systems with adversarial inputs. Given a set of state and input constraints, and treating the inputs in best-case and/or worst-case fashion, we construct invariant, viable and discriminating sets, which must therefore under-approximate the invariant, viable and discriminating kernels respectively. The sets are constructed by scaling zonotopes represented in center-generator form. The scale factors are found through efficient convex optimizations. The results are demonstrated on two toy examples and a six dimensional nonlinear longitudinal model of a quadrotor. |
| title | Invariant, Viability and Discriminating Kernel Under-Approximation via Zonotope Scaling |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/1901.01006 |