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arXiv · 1907.12075

Data-driven computation of invariant sets of discrete time-invariant black-box systems

Zheming Wang·Raphaël M. Jungers
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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.

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Zheming Wang, Raphaël M. Jungers. 2019-07-28. Data-driven computation of invariant sets of discrete time-invariant black-box systems. https://doi.org/10.1109/lcsys.2020.3001882

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