Control Barrier Functionals: Safety-critical Control for Time Delay Systems

TL;DR

This paper extends control barrier functions to time delay systems by introducing control barrier functionals, enabling formal safety guarantees and safe control synthesis in systems with delays.

Contribution

It develops a novel theoretical framework for safety-critical control of delay systems using control barrier functionals, handling multiple and distributed delays.

Findings

Framework provides formal safety guarantees for delay systems.

Control synthesis via affine constraints ensures safety.

Numerical simulations demonstrate effectiveness.

Abstract

This work presents a theoretical framework for the safety-critical control of time delay systems. The theory of control barrier functions, that provides formal safety guarantees for delay-free systems, is extended to systems with state delay. The notion of control barrier functionals is introduced to attain formal safety guarantees, by enforcing the forward invariance of safe sets defined in the infinite dimensional state space. The proposed framework is able to handle multiple delays and distributed delays both in the dynamics and in the safety condition, and provides an affine constraint on the control input that yields provable safety. This constraint can be incorporated into optimization problems to synthesize pointwise optimal and provable safe controllers. The applicability of the proposed method is demonstrated by numerical simulation examples.