Control Barrier Function Based Quadratic Programs for Safety Critical Systems

By Aaron D. Ames, Xiangru Xu, Jessy W. Grizzle, Paulo Tabuada. IEEE Transactions on Automatic Control, 2016

2,651 citations recorded by the source corpus.

Safety critical systems involve the tight coupling between potentially conflicting control objectives and safety constraints. As a means of creating a formal framework for controlling systems of this form, and with a view toward automotive applications, this paper develops a methodology that allows safety conditions—expressed as control barrier functions—to be unified with performance objectives—expressed as control Lyapunov functions—in the context of real-time optimization-based controllers. Safety conditions are specified in terms of forward invariance of a set, and are verified via two novel generalizations of barrier functions; in each case, the existence of a barrier function satisfying Lyapunov-like conditions implies forward invariance of the set, and the relationship between these two classes of barrier functions is characterized. In addition, each of these formulations yields a notion of control barrier function (CBF), providing inequality constraints in the control input that, when satisfied, again imply forward invariance of the set. Through these constructions, CBFs can naturally be unified with control Lyapunov functions (CLFs) in the context of a quadratic program (QP); this allows for the achievement of control objectives (represented by CLFs) subject to conditions on the admissible states of the system (represented by CBFs). The mediation of safety and performance through a QP is demonstrated on adaptive cruise control and lane keeping, two automotive control problems that present both safety and performance considerations coupled with actuator bounds.

Subfields: Automotive Engineering, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/291a176dc906f31e8faf760911a61f0ca9bde444

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Automotive Engineering

In Control and Systems Engineering

Citations in the corpus

End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks (2019, background): “The existence of a CBF implies that there exists a deterministic controller u CBF : S → A such that the set C is forward invariant for system (1) (Agrawal and Sreenath 2017; Ames et al. 2017).”
Input-to-State Safety With Control Barrier Functions (2018, background): “In this section, we will study barrier functions and also state their relationships with forward invariance of a set (see [2], wherein the version we considered was called zeroing barrier functions).”
Control Barrier Functions for Signal Temporal Logic Tasks (2019, background): “A time-varying candidate control barrier function implies that C(t) is non-empty for each t ∈ [t0, t1], which is the standard assumption for a time-independent function to be a candidate control barrier function [12], [13].”
Control Barrier Functions: Theory and Applications (2019, background): “The main result of [21], and the main result with regard to control barrier functions, is that the existence of a control barrier function implies that the control system is safe:”
Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Function (2020, methodology): “ermore, a safety-critical control design for continuous-time systems was proposed by unifying a control Lyapunov function (CLF) and a control barrier function through a quadratic program (CLF-CBF-QP) [2], [15]. This method could be deployed as a real-time optimization-based controller with safety-cr”
Safe Control With Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction Methods for Robotics and Control (2022, methodology): “Similarly to constrained MPC, certificate-based controllers, such as the QP given in (10a), can easily adapt to actuator limits [20].”