Verification and Synthesis of Control Barrier Functions

Understand

Control systems often must satisfy strict safety requirements over an extended operating lifetime.

• Control Barrier Functions (CBFs) are a promising recent approach to constructing simple and safe control policies.
• This paper proposes a framework for verifying that a CBF guarantees safety for all time and synthesizing CBFs with verifiable safety in polynomial control systems.
• Our approach is to show that safety of CBFs is equivalent to the non-existence of solutions to a family of polynomial equations, and then prove that this nonexistence is equivalent to a pair of sum-of-squares constraints via the Positivstellensatz of algebraic geometry.