Title:
Robustness of Control Barrier Functions for Safety Critical Control
Robustness of Control Barrier Functions for Safety Critical Control
Author(s)
Xu, Xiangru
Tabuada, Paulo
Grizzle, Jessy W.
Ames, Aaron D.
Tabuada, Paulo
Grizzle, Jessy W.
Ames, Aaron D.
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Abstract
Barrier functions (also called certificates) have been an important tool for the verification of hybrid systems, and have also played important roles in optimization and multi-objective
control. The extension of a barrier function to a controlled system results in a control
barrier function. This can be thought of as being analogous to how Sontag extended Lyapunov
functions to control Lypaunov functions in order to enable controller synthesis for stabilization
tasks. A control barrier function enables controller synthesis for safety requirements specified
by forward invariance of a set using a Lyapunov-like condition. This paper develops several
important extensions to the notion of a control barrier function. The first involves robustness
under perturbations to the vector field defining the system. Input-to-State stability conditions
are given that provide for forward invariance, when disturbances are present, of a "relaxation"
of set rendered invariant without disturbances. A control barrier function can be combined with
a control Lyapunov function in a quadratic program to achieve a control objective subject to
safety guarantees. The second result of the paper gives conditions for the control law obtained
by solving the quadratic program to be Lipschitz continuous and therefore to gives rise to
well-defined solutions of the resulting closed-loop system.
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Date Issued
2015
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