Systematic Design of Discrete-Time Control Barrier Functions Using Maximal Output Admissible Sets

Abstract

This paper provides an approach to design control barrier functions (CBFs) using the notion of dynamic safety margins (DSMs). In particular, it is shown that DSMs are CBFs for an augmented system. The proposed approach can handle multiple state and input constraints using the control-sharing property of CBFs. Moreover, it makes no assumption on the relative degree of the constraints. Numerical simulations show that the method outperforms existing DSM-based approaches, while also guaranteeing safety and recursive feasibility.