Scenario-Based Set Invariance Verification for Black-Box Nonlinear Systems
Zheming Wang, Raphaël M. Jungers
Abstract
We consider the problem of set invariance verification in black-box nonlinear systems without analytic dynamical models. A data-driven set invariance verification approach relying on the observation of trajectories is proposed to determine almost-invariant sets, which are invariant almost everywhere except possibly in a small subset. With these observations, scenario optimization problems are formulated. 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 by the use of a polynomial classifier. The practical performance of the proposed data-driven framework is illustrated by numerical examples.