Transfer of Safety Controllers Through Learning Deep Inverse Dynamics Model

Control barrier certificates have proven effective in formally guaranteeing the safety of the control systems. However, designing a control barrier certificate is a time-consuming and computationally expensive endeavor that requires expert input in the form of domain knowledge and mathematical maturity. Additionally, when a system undergoes slight changes, the new controller and its correctness certificate need to be recomputed, incurring similar computational challenges as those faced during the design of the original controller. Prior approaches have utilized transfer learning to transfer safety guarantees in the form of a barrier certificate while maintaining the control invariant. Unfortunately, in practical settings, the source and the target environments often deviate substantially in their control inputs, rendering the aforementioned approach impractical. To address this challenge, we propose integrating \emph{inverse dynamics} -- a neural network that suggests required action given a desired successor state -- of the target system with the barrier certificate of the source system to provide formal proof of safety. In addition, we propose a validity condition that, when met, guarantees correctness of the controller. We demonstrate the effectiveness of our approach through three case studies.