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Control Barrier Functions (CBFs) aim to ensure safety by constraining the control input at each time step so that the system state remains within a desired safe region. This paper presents a framework for CBFs in stochastic systems in the…

Optimization and Control · Mathematics 2020-10-20 Andrew Clark

Control barrier functions (CBFs) play a critical role in the design of safe optimization-based controllers for control-affine systems. Given a CBF associated with a desired ``safe'' set, the typical approach consists in embedding CBF-based…

Systems and Control · Electrical Eng. & Systems 2024-09-12 Yiting Chen , Pol Mestres , Jorge Cortes , Emiliano Dall'Anese

Learning-based control with safety guarantees usually requires real-time safety certification and modifications of possibly unsafe learning-based policies. The control barrier function (CBF) method uses a safety filter containing a…

Systems and Control · Electrical Eng. & Systems 2024-10-25 Kanghui He , Shengling Shi , Ton van den Boom , Bart De Schutter

Correct-by-construction techniques, such as control barrier functions (CBFs), can be used to guarantee closed-loop safety by acting as a supervisor of an existing or legacy controller. However, supervisory-control intervention typically…

Systems and Control · Computer Science 2018-05-03 Yuxiao Chen , Ayonga Hereid , Huei Peng , Jessy Grizzle

In safety-critical control systems, ensuring both system safety and smooth control input is essential for practical deployment. Existing Control Barrier Function (CBF) frameworks, especially High-Order CBFs (HOCBFs), effectively enforce…

Systems and Control · Electrical Eng. & Systems 2026-03-11 Shuo Liu , Wei Xiao , Calin A. Belta

This paper considers the general problem of transitioning theoretically safe controllers to hardware. Concretely, we explore the application of control barrier functions (CBFs) to sampled-data systems: systems that evolve continuously but…

Systems and Control · Electrical Eng. & Systems 2020-05-14 Andrew Singletary , Yuxiao Chen , Aaron D. Ames

Control Barrier Functions (CBFs) have emerged as a powerful paradigm in control theory, providing a principled approach to enforcing safety-critical constraints in dynamic systems. This survey paper comprehensively explores the foundational…

Systems and Control · Electrical Eng. & Systems 2024-08-27 Promit Panja

Adaptive control provides closed-loop stability and reference tracking for uncertain dynamical systems through online parameter adaptation. These properties alone, however, do not ensure safety in the sense of forward invariance of state…

Systems and Control · Electrical Eng. & Systems 2026-03-17 Johannes Autenrieb , Peter A. Fisher , Anuradha Annaswamy

Safety is of paramount importance in control systems to avoid costly risks and catastrophic damages. The control barrier function (CBF) method, a promising solution for safety-critical control, poses a new challenge of enhancing control…

Systems and Control · Electrical Eng. & Systems 2025-03-26 Shengbo Wang , Ke Li , Zheng Yan , Zhenyuan Guo , Song Zhu , Guanghui Wen , Shiping Wen

Safety filters based on control barrier functions (CBFs) have become a popular method to guarantee safety for uncertified control policies, e.g., as resulting from reinforcement learning. Here, safety is defined as staying in a pre-defined…

Systems and Control · Electrical Eng. & Systems 2024-04-19 Lukas Brunke , Siqi Zhou , Mingxuan Che , Angela P. Schoellig

This tutorial provides a critical review of the practical application of Control Barrier Functions (CBFs) in robotic safety. While the theoretical foundations of CBFs are well-established, I identify a recurring gap between the mathematical…

Robotics · Computer Science 2026-03-10 Taekyung Kim

Control Barrier Functions (CBF) have provided a very versatile framework for the synthesis of safe control architectures for a wide class of nonlinear dynamical systems. Typically, CBF-based synthesis approaches apply to systems that…

Systems and Control · Electrical Eng. & Systems 2024-02-15 Shuo Yang , Mitchell Black , Georgios Fainekos , Bardh Hoxha , Hideki Okamoto , Rahul Mangharam

Connected automated vehicles have shown great potential to improve the efficiency of transportation systems in terms of passenger comfort, fuel economy, stability of driving behavior and mitigation of traffic congestions. Yet, to deploy…

Systems and Control · Electrical Eng. & Systems 2023-09-04 Tamas G. Molnar , Gabor Orosz , Aaron D. Ames

This paper investigates the control barrier function (CBF) based safety-critical control for continuous nonlinear control affine systems using the more efficient online algorithms through time-varying optimization. The idea lies in that…

Systems and Control · Electrical Eng. & Systems 2023-03-21 Shengbo Wang , Shiping Wen , Yin Yang , Yuting Cao , Kaibo Shi , Tingwen Huang

In recent years, the analysis of a control barrier function has received considerable attention because it is helpful for the safety-critical control required in many control application problems. While the extension of the analysis to a…

Optimization and Control · Mathematics 2024-04-18 Yuki Nishimura , Kenta Hoshino

Safety is one of the fundamental problems in robotics. Recently, a quadratic program-based control barrier function (CBF) method has emerged as a way to enforce safety-critical constraints. Together with control Lyapunov function (CLF), it…

Systems and Control · Electrical Eng. & Systems 2022-01-03 Jun Zeng , Bike Zhang , Zhongyu Li , Koushil Sreenath

This work develops a robust adaptive control strategy for discrete-time systems using Control Barrier Functions (CBFs) to ensure safety under parametric model uncertainty and disturbances. A key contribution of this work is establishing a…

Systems and Control · Electrical Eng. & Systems 2026-02-05 Changrui Liu , Anil Alan , Shengling Shi , Bart De Schutter

This contribution introduces a centralized input constrained optimal control framework based on multiple control barrier functions (CBFs) to coordinate connected and automated agents at intersections. For collision avoidance, we propose a…

Optimization and Control · Mathematics 2022-07-12 Alexander Katriniok

Control Barrier Functions (CBFs) have been demonstrated to be a powerful tool for safety-critical controller design for nonlinear systems. Existing design paradigms do not address the gap between theory (controller design with continuous…

Systems and Control · Electrical Eng. & Systems 2022-06-15 Andrew J. Taylor , Victor D. Dorobantu , Ryan K. Cosner , Yisong Yue , Aaron D. Ames

Endowing nonlinear systems with safe behavior is increasingly important in modern control. This task is particularly challenging for real-life control systems that must operate safely in dynamically changing environments. This paper…

Systems and Control · Electrical Eng. & Systems 2022-12-06 Tamas G. Molnar , Adam K. Kiss , Aaron D. Ames , Gábor Orosz