Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Equilibria and their stability do not depend on the
control barrier function in safe optimization-based
control
Y. Chen, P. Mestres, J. Cortés, E. Dall'Anese
IEEE Access, submitted
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 desired ``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); 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 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 and
controllers based on both CBF and control Lyapunov
functions (CLFs), 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.
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