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

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.

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)

References in corpus (1)

• Convex computation of the maximum controlled invariant set for polynomial control systems

Cited by in corpus (8)

• Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview
• On Recurrent Neural Networks for learning-based control: recent results and ideas for future developments
• Towards Guaranteed Safety Assurance of Automated Driving Systems with Scenario Sampling: An Invariant Set Perspective (Extended Version)
• A data-driven method for computing polyhedral invariant sets of black-box switched linear systems
• Guarantees for Real Robotic Systems: Unifying Formal Controller Synthesis and Reachset-Conformant Identification
• A Formal Characterization of Black-Box System Safety Performance with Scenario Sampling
• Computation of invariant sets via immersion for discrete-time nonlinear systems
• Probabilistic stabilizability certificates for a class of black-box linear systems