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Data-driven computation of invariant sets of discrete time-invariant black-box systems
- Publication Year :
- 2019
-
Abstract
- We consider the problem of computing the maximal invariant set of discrete-time black-box nonlinear systems without analytic dynamical models. Under the assumption that the system is asymptotically stable, the maximal invariant set coincides with the domain of attraction. A data-driven framework relying on the observation of trajectories is proposed to compute almost-invariant sets, which are invariant almost everywhere except a small subset. Based on these observations, scenario optimization problems are formulated and solved. We show that probabilistic invariance guarantees on the almost-invariant sets can be established. To get explicit expressions of such sets, a set identification procedure is designed with a verification step that provides inner and outer approximations in a probabilistic sense. The proposed data-driven framework is illustrated by several numerical examples.<br />Comment: A shorter version with the title "Scenario-based set invariance verification for black-box nonlinear systems" is published in the IEEE Control Systems Letters (L-CSS)
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1907.12075
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1109/LCSYS.2020.3001882