838 research outputs found
A De Giorgi Iteration-based Approach for the Establishment of ISS Properties for Burgers' Equation with Boundary and In-domain Disturbances
This note addresses input-to-state stability (ISS) properties with respect to
(w.r.t.) boundary and in-domain disturbances for Burgers' equation. The
developed approach is a combination of the method of De~Giorgi iteration and
the technique of Lyapunov functionals by adequately splitting the original
problem into two subsystems. The ISS properties in -norm for Burgers'
equation have been established using this method. Moreover, as an application
of De~Giorgi iteration, ISS in -norm w.r.t. in-domain disturbances
and actuation errors in boundary feedback control for a 1- {linear}
{unstable reaction-diffusion equation} have also been established. It is the
first time that the method of De~Giorgi iteration is introduced in the ISS
theory for infinite dimensional systems, and the developed method can be
generalized for tackling some problems on multidimensional spatial domains and
to a wider class of nonlinear {partial differential equations (PDEs)Comment: This paper has been accepted for publication by IEEE Trans. on
Automatic Control, and is available at
http://dx.doi.org/10.1109/TAC.2018.2880160. arXiv admin note: substantial
text overlap with arXiv:1710.0991
Event-triggered Boundary Control of a Class of Reaction-Diffusion PDEs with Time-dependent Reactivity
This paper presents an event-triggered boundary control strategy for a class
of reaction-diffusion PDEs with time-varying reactivity under Robin actuation.
The control approach consists of a backstepping full-state feedback boundary
controller and a dynamic event-triggering condition, which determines the time
instants when the control input needs to be updated. It is proved that under
the proposed event-triggered boundary control approach, there is a uniform
minimal dwell-time between two event times. Furthermore, the well-posedness and
the global exponential convergence of the closed-loop system to zero in
-sense are established. A simulation is conducted to validate the
theoretical developments
- …