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Control Barrier Function Based Quadratic Programs for Safety Critical Systems

Ames, Aaron D. and Xu, Xiangru and Grizzle, Jessy W. and Tabuada, Paulo (2017) Control Barrier Function Based Quadratic Programs for Safety Critical Systems. IEEE Transactions on Automatic Control, 62 (8). pp. 3861-3876. ISSN 0018-9286. doi:10.1109/TAC.2016.2638961.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Ames, Aaron D.0000-0003-0848-3177
Xu, Xiangru0000-0003-1367-6790
Grizzle, Jessy W.0000-0001-7586-0142
Tabuada, Paulo0000-0002-3417-0951
Additional Information:© 2016 IEEE. Manuscript received April 4, 2016; accepted November 14, 2016. Date of publication December 13, 2016; date of current version July 26, 2017. This work was supported by NSF CPS Awards 1239055, 1239037 and 1239085. The work of X. Xu was supported in part by a gift of the Ford Motor Company. Recommended by Associate Editor S. Tarbouriech.
Funding AgencyGrant Number
Ford Motor CompanyUNSPECIFIED
Subject Keywords:Barrier function, control Lyapunov function, nonlinear control, quadratic program, safety, set invariance
Issue or Number:8
Record Number:CaltechAUTHORS:20170726-152043029
Persistent URL:
Official Citation:A. D. Ames, X. Xu, J. W. Grizzle and P. Tabuada, "Control Barrier Function Based Quadratic Programs for Safety Critical Systems," in IEEE Transactions on Automatic Control, vol. 62, no. 8, pp. 3861-3876, Aug. 2017. doi: 10.1109/TAC.2016.2638961
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79450
Deposited On:26 Jul 2017 22:35
Last Modified:15 Nov 2021 17:48

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