Control Barrier Functions in Sampled-Data Systems

TL;DR

This paper develops less conservative conditions for ensuring safety in sampled-data systems using barrier functions, enabling more effective control synthesis with fixed sampling intervals.

Contribution

It introduces new metrics and three approaches for forward invariance, improving upon existing methods for sampled-data control systems.

Findings

Proposed conditions are less conservative than previous methods.

Enables implementation of barrier functions previously infeasible with fixed time-steps.

Simulation results demonstrate improved control synthesis capabilities.

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.