Patching Approximately Safe Value Functions Leveraging Local Hamilton-Jacobi Reachability Analysis

Understand

Safe value functions, such as control barrier functions, characterize a safe set and synthesize a safety filter, overriding unsafe actions, for a dynamic system.

• While function approximators like neural networks can synthesize approximately safe value functions, they typically lack formal guarantees.
• In this paper, we propose a local dynamic programming-based approach to "patch" approximately safe value functions to obtain a safe value function.
• This algorithm, HJ-Patch, produces a novel value function that provides formal safety guarantees, yet retains the global structure of the initial value function.