Neural Koopman Control Barrier Functions for Safety-Critical Control of Unknown Nonlinear Systems

TL;DR

This paper introduces a data-driven framework that uses Koopman operator theory to synthesize safe controllers for unknown nonlinear systems by learning a bilinear system and a corresponding control barrier function, ensuring safety through quadratic programming.

Contribution

It proposes a novel method combining Koopman operator theory with control barrier functions for safety-critical control of unknown nonlinear systems, with theoretical error bounds and practical validation.

Findings

Validated approach through numerical simulations

Learned CBF guarantees safety of unknown systems

Error bounds improve with Lipschitz constants

Abstract

We consider the problem of synthesis of safe controllers for nonlinear systems with unknown dynamics using Control Barrier Functions (CBF). We utilize Koopman operator theory (KOT) to associate the (unknown) nonlinear system with a higher dimensional bilinear system and propose a data-driven learning framework that uses a learner and a falsifier to simultaneously learn the Koopman operator based bilinear system and a corresponding CBF. We prove that the learned CBF for the latter bilinear system is also a valid CBF for the unknown nonlinear system by characterizing the $\ell^2$-norm error bound between these two systems. We show that this error can be partially tuned by using the Lipschitz constant of the Koopman based observables. The CBF is then used to formulate a quadratic program to compute inputs that guarantee safety of the unknown nonlinear system. Numerical simulations are presented to validate our approach.