A Learning-Based Method for Computing Control Barrier Functions of Nonlinear Systems With Control Constraints

摘要

Verifying the safety of states and designing a safety controller are very important for safety critical systems (for example, robotic and automotive systems). Since the reachable set of a state is hard to calculate online, it is difficult to determine whether the current state will enter the unsafe set in the future. Thus, the safe set of a system is usually obtained by calculating the forward invariant set offline. For control affine systems, the control barrier function provides a linear safety constraint on the control, which helps us obtain safety control online. However, the computation of control barrier functions is recognized as difficult, and existing methods make over-approximations or are only applicable to problems without control constraints. In this letter, we propose a learning-based method to compute the control barrier function for nonlinear control affine systems with control constraints. The method consists of a constraint satisfaction (CS) algorithm and a set expansion (SE) algorithm. The CS algorithm computes the control barrier function that satisfies the constraints, and the SE algorithm expands the volume of the safe set. The numerical results demonstrate that our algorithm outperforms existing methods and can improve existing control barrier functions.