General DAE-aware CBF framework for safety-filter design and verification

Develop a general framework for DAE-aware control barrier functions that simultaneously addresses safety-filter design and formal verification for differential-algebraic equation systems.

Background

The paper discusses existing methods for safety verification and control synthesis in differential-algebraic equation (DAE) systems. Reachability and barrier-certificate approaches provide offline verification or certification, while existing control methods do not construct real-time safety filters that account for algebraic constraints. Prior control-barrier-function work for DAEs also does not explicitly derive how control inputs ensure invariance of the algebraic constraint manifold or provide a method for verifying candidate barrier functions.

The unresolved problem is to combine these capabilities in a general DAE-aware control-barrier-function framework that supports both real-time safety-filter construction and formal verification of safety, manifold compatibility, and feasibility.