Control Barrier Proximal Dynamics: A Contraction Theoretic Approach for Safety Verification

In this letter, we present a computationally-efficient barrier function-based contraction-theoretic approach for safety verification. We adopt a dynamical system approach towards Control Barrier Function (CBF)-based Quadratic Programming (QP). To mitigate the computational complexity of online solutions to time-varying convex optimization, we integrate tools from contraction theory and proximal primal-dual gradient dynamics (PDGD) to provide an arbitrarily close approximation of the optimal solution. Subsequently, we adopt this result for the CBF-based QP, offering a computationally-efficient and scalable safe control design termed Control Barrier Proximal Dynamics (CBPD). The contractivity of the CBPD is then leveraged to characterize the safety of the system. We demonstrate that adopting CBPD under a technical assumption guarantees the safety specifications of the system with a bounded violation margin, which can be made arbitrarily small. Additionally, a computational analysis depicts substantial improvements in efficiency and scalability compared to the state-of-the-art. Finally, we evaluate the effectiveness of the proposed method through the simulation of a battery management problem with electro-thermal constraints.