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

Abstract

This paper introduces a novel discrete-time control barrier function (DCBF) that stems directly from discrete-time set invariance theory. The proposed DCBF provides necessary and sufficient conditions for certifying control invariance and can be used to synthesize a constrained control policy. Moreover, the DCBF can be constructed for arbitrary sets of state and input constraints by taking advantage of maximal output admissible set theory. The resulting DCBF-based controller is proven to be safe and recursively feasible. Numerical examples showcase the effectiveness of the scheme by comparing it to existing constrained control approaches.