Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Control barrier function-based safety filters:
characterization of undesired equilibria, unbounded
trajectories, and limit cycles
P. Mestres, Y. Chen, E. Dall'Anese, J. Cortés
Journal of Nonlinear Science, submitted
Abstract
This paper focuses on "safety filters"
designed based on Control Barrier Functions (CBFs):
these are modifications of a nominal stabilizing
controller typically utilized in safety-critical
control applications to render a given subset of
states forward invariant. The paper investigates the
dynamical properties of the closed-loop systems,
with a focus on characterizing undesirable behaviors
that may emerge due to the use of CBF-based
filters. These undesirable behaviors include
unbounded trajectories, limit cycles, and undesired
equilibria, which can be locally stable and even
form a continuum. Our analysis offer the following
contributions: (i) conditions under which
trajectories remain bounded and (ii) conditions
under which limit cycles do not exist; (iii) we show
that undesired equilibria can be characterized by
solving an algebraic equation, and (iv) we provide
examples that show that asymptotically stable
undesired equilibria can exist for any choice of
nominal controller and design parameters of the
safety filter (even for convex safe sets). Further,
for the specific class of planar systems, (v) we
provide explicit formulas for the total number of
undesired equilibria and the proportion of saddle
points and asymptotically stable equilibria, and
(vi) in the case of linear planar systems, we
present an exhaustive analysis of their global
stability properties. Examples throughout the paper
illustrate the results.
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