Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Performance-barrier-based event-triggered boundary
control of a class of reaction-diffusion PDEs
B. Rathnayake, M. Diagne, J. Cortés,
M. Krstic
Automatica, submitted
Abstract
We employ the recent performance-barrier-based
event-triggered control (P-ETC) for stabilization of
a class of reaction-diffusion PDEs with Dirichlet
boundary actuation. Rather than insisting on a
strictly monotonic decrease of the Lyapunov function
for the closed-loop system, P-ETC allows the
Lyapunov function to increase as long as it remains
below an acceptable performance barrier. This
approach integrates a performance residual-the
difference between the value of the performance
barrier and the Lyapunov function-into the
triggering mechanism. The integration adds
flexibility and results in fewer control updates
than with strategies that demand a monotonic
decrease of the Lyapunov function. Our P-ETC PDE
backstepping designs ensure global exponential
convergence in the spatial L2 norm, without
encountering the Zeno phenomenon. To avoid
continuous monitoring of the triggering function, we
develop periodic event-triggered and self-triggered
variants (P-PETC and P-STC, respectively) of
P-ETC. P-PETC only requires periodic evaluation
whereas the P-STC preemptively computes the time of
the next event at the current event time using the
system model and the continuously available system
states. P-PETC and P-STC also ensure a Zeno-free
behavior and deliver performance equivalent to that
of continuous-time P-PETC, which requires a
continuous computation of the triggering function,
in addition to the continuous sensing of the
state. We provide numerical simulations to
demonstrate the effectiveness of our technique
against the regular event-triggered boundary control
design, the latter being associated with strictly
decreasing Lyapunov functions.
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