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

Kiss, Ádám K. and Das, Ersin and Molnár, Tamás G. and Ames, Aaron D. (2026) Integral Control Barrier Functions with Input Delay: Prediction, Feasibility, and Robustness. IEEE CONTROL SYSTEMS LETTERS, 10. pp. 2077-2082. ISSN 2475-1456

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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 for the effect of delays, while ensuring feasibility when state and input constraints are imposed jointly. To this end, we embed predictor feedback into the ICBF framework, making controllers operate on the predicted state. 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. © 2017 IEEE.

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