Control Barrier Functions in Sampled-Data Systems

Abstract

This paper presents conditions for ensuring forward invariance of safe sets under sampled-data system dynamics with piecewise-constant controllers and fixed time-steps. First, we introduce two different metrics to compare the conservativeness of sufficient conditions on forward invariance under piecewise-constant controllers. Then, we propose three approaches for guaranteeing forward invariance, two motivated by continuous-time barrier functions, and one motivated by discrete-time barrier functions. All proposed conditions are control affine, and thus can be incorporated into quadratic programs for control synthesis. We show that the proposed conditions are less conservative than those in earlier studies, and show via simulation how this enables the use of barrier functions that are impossible to implement with the desired time-step using existing methods.

arXiv commentPublished in IEEE Control Systems Letters, 6 pages. See prior version for additional theorem not included in final version

References in corpus (4)

• Control Barrier Function Based Quadratic Programs for Safety Critical Systems
• OSQP: An Operator Splitting Solver for Quadratic Programs
• Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Function
• Tractable Compositions of Discrete-Time Control Barrier Functions with Application to Lane Keeping and Obstacle Avoidance

Cited by in corpus (5)

• Safety-Critical Control for Autonomous Systems: Control Barrier Functions via Reduced-Order Models
• Safe and Robust Observer-Controller Synthesis using Control Barrier Functions
• Control Barrier Function Meets Interval Analysis: Safety-Critical Control with Measurement and Actuation Uncertainties
• A Constructive Method for Designing Safe Multirate Controllers for Differentially-Flat Systems
• SHIELD: Safety on Humanoids via CBFs In Expectation on Learned Dynamics