Sample Efficient Certification of Discrete-Time Control Barrier Functions
This work addresses a specific bottleneck in control theory for safety-critical systems, but it appears incremental as it builds on existing scenario-based methods.
The paper tackles the problem of verifying Control Barrier Functions (CBFs) for safety certification in dynamical systems by proposing a sample-efficient certification algorithm based on Lipschitz arguments, validated through a numerical example.
Control Invariant (CI) sets are instrumental in certifying the safety of dynamical systems. Control Barrier Functions (CBFs) are effective tools to compute such sets, since the zero sublevel sets of CBFs are CI sets. However, computing CBFs generally involves addressing a complex robust optimization problem, which can be intractable. Scenario-based methods have been proposed to simplify this computation. Then, one needs to verify if the CBF actually satisfies the robust constraints. We present an approach to perform this verification that relies on Lipschitz arguments, and forms the basis of a certification algorithm designed for sample efficiency. Through a numerical example, we validated the efficiency of the proposed procedure.