Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Independence of closed-loop equilibria and stability from the choice of
control barrier function for a given safe set
Y. Chen, P. Mestres, J. Cortés, E. Dall'Anese
Automatica (2026), to appear
Abstract
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 given,
predefined "safe" set, the typical approach consists in embedding
CBF-based constraints into the optimization problem defining the
control law to enforce forward invariance of the safe set. While this
approach effectively guarantees safety for a given CBF, the CBF-based
control law can introduce undesirable equilibrium points (i.e., points
that are not equilibria of the original system). Given that there
exist many different CBFs associated with a given fixed safe set, open
questions remain on how the choice of CBF influences the number and
locations of undesirable equilibria and, in general, the dynamics of
the closed-loop system. This paper investigates how the choice of CBF
impacts the dynamics of the closed-loop system and shows that: (i) The
choice of CBF does not affect the number, location, and (local)
stability properties of the equilibria in the interior of the safe
set; (ii) undesirable equilibria only appear on the boundary of the
safe set; and, (iii) the number and location of undesirable equilibria
for the closed-loop system do not depend of the choice of the
CBF. Additionally, for the well-established safety filters, we show
that the stability properties of equilibria of the closed-loop system
are independent of the choice of the CBF and of the associated
extended class-K function, provided that the CBFs are chosen from the
same equivalence class.
pdf
Mechanical and Aerospace Engineering,
University of California, San Diego
9500 Gilman Dr,
La Jolla, California, 92093-0411
Ph: 1-858-822-7930
Fax: 1-858-822-3107
cortes at ucsd.edu
Skype id:
jorgilliyo