Integral Control Barrier Functions with Input Delay: Prediction, Feasibility, and Robustness

TL;DR

This paper introduces a novel control framework that uses integral control barrier functions with predictor feedback to ensure safety and feasibility in nonlinear systems with input delays, validated through adaptive cruise control.

Contribution

It develops a delay-compensating control method using predictor feedback and ICBFs, providing feasibility conditions and robustness to delay uncertainties.

Findings

Ensures safety under input delays with a quadratic program approach.

Provides a closed-form feasibility condition for joint state and input constraints.

Demonstrates effectiveness on an adaptive cruise control system with actuation delay.

Abstract

Time delays in feedback control loops can cause controllers to respond too late, and with excessively large corrective actions, leading to unsafe behavior (violation of state constraints) and controller infeasibility (violation of input constraints). To address this problem, we develop a safety-critical control framework for nonlinear systems with input delay using dynamically defined (integral) controllers. Building on the concept of Integral Control Barrier Functions (ICBFs), we concurrently address two fundamental challenges: compensating the effect of delays, while ensuring feasibility when state and input constraints are imposed jointly. To this end, we embed predictor feedback into a dynamically defined control law to compensate for delays, with the predicted state evolving according to delay-free dynamics. Then, utilizing ICBFs, we formulate a quadratic program for safe control design. For systems subject to simultaneous state and input constraints, we derive a closed-form feasibility condition for the resulting controller, yielding a compatible ICBF pair that guarantees forward invariance under delay. We also address robustness to prediction errors (e.g., caused by delay uncertainty) using tunable robust ICBFs. Our approach is validated on an adaptive cruise control example with actuation delay.