Systematic Design of Discrete-Time Control Barrier Functions Using Maximal Output Admissible Sets
Victor Freire, Marco M. Nicotra
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.
Topics & Concepts
Discrete time and continuous timeControl theory (sociology)Controller (irrigation)Set (abstract data type)Function (biology)Scheme (mathematics)State (computer science)Control (management)Mathematical optimizationComputer scienceSet theoryMathematicsAlgorithmAgronomyMathematical analysisArtificial intelligenceStatisticsProgramming languageEvolutionary biologyBiologyAdvanced Control Systems OptimizationFault Detection and Control SystemsStability and Control of Uncertain Systems