Predictive control barrier functions: Enhanced safety mechanisms for learning-based control

TL;DR

This paper introduces a soft-constrained predictive control approach with a control barrier function to enhance safety guarantees in learning-based control systems, ensuring feasibility and stability.

Contribution

It proposes an auxiliary predictive control problem with constraint tightening and a terminal control barrier function to improve safety filter robustness.

Findings

The auxiliary problem is always feasible at each time step.

It asymptotically stabilizes the feasible set of the safety filter.

Numerical examples demonstrate the effectiveness of the approach.

Abstract

While learning-based control techniques often outperform classical controller designs, safety requirements limit the acceptance of such methods in many applications. Recent developments address this issue through so-called predictive safety filters, which assess if a proposed learning-based control input can lead to constraint violations and modifies it if necessary to ensure safety for all future time steps. The theoretical guarantees of such predictive safety filters rely on the model assumptions and minor deviations can lead to failure of the filter putting the system at risk. This paper introduces an auxiliary soft-constrained predictive control problem that is always feasible at each time step and asymptotically stabilizes the feasible set of the original safety filter, thereby providing a recovery mechanism in safety-critical situations. This is achieved by a simple constraint tightening in combination with a terminal control barrier function. By extending discrete-time control barrier function theory, we establish that the proposed auxiliary problem provides a `predictive' control barrier function. The resulting algorithm is demonstrated using numerical examples.