- George Avalos, University of Nebraska-Lincoln
- Francesca Bucci, Universita' di Firenze
"Novel directions in control of evolutionary PDE problems"
intend that our minisymposia should deal with topics concerning the
mathematical control of partial di¤erential equation (PDE) systems. In
particular, the emphasis here will be on those PDEs which have been
used to describe various phenomena in the physical sciences and
It is anticipated that our Speakers will broach in our Sessions ostensibly classical control theoretic
subjects, which however will be framed within a modern PDE setting, and rigorously developed
by state of the art time/frequency domain multiplier methods and pseudodifferential/PDE control techniques.
the participants in our Minisymposia will be internationally recognized
pioneers and contributors in the mathematical control of in
In addition to the intrinsic merit of our
proposed forum to have renowned experts in PDE control theory present
their recent research, there is the possibility for further advancement
in the field, by virtue of the
opportunity provided in our Minisymposia for discussion and future collaboration.
Examples of such problems which would fall under the scope of our proposed Sessions include
The optimal control of PDEs with respect to given quadratic or
non-quadratic cost functionals; with possible characterizations of
these optimal controls being provided via appropriate solutions to the
In particular, there would be an emphasis on PDE
systems whose characteristics are of mixed type; in which case
optimal control theories currently found in the literature would not
avail in the associated PDE and optimzation analysis, inasmuch as
existing PDE optimal control results are critically dependent upon the
characteristics of the PDE dynamics involved.
Examples of such
mixed-type PDE control problems include uid-structure PDE systems with
boundary control effected in the so-called Polya tensor; and composite
sandwichstructures which are composed of a multiplicity of elastic
PDEs, some of which are under the influence of boundary control.
Stabilization of given PDE dynamics through the agency of
dissipation-enhancing boundary feedback control mechanisms. Along with
those uncontrolled PDE systems which exhibit a underlying conservation
of energy, it is possible that the free dynamics which are to be
feedback- controlled would actually manifest heat-generating (feedback)
sources (or an anti-conservation, if you will). The control objective
would then be to demonstrate that the incorporation of either boundary
and/or strictly localized interior control, each in feedback form, will
induce some bene
ficient stabilizing effect upon the controlled
PDE solutions, in long time. Such a stabilization could be realized as
an outright uniform decay of the PDE solutions, as time goes to
nity; or possibly a global attracting set to which the solutions
tend in the course of evolution. (The latter possibility would arise in
the case of PDE systems under the inuence of non-Lipschitz and
(iii) The steering or
controlling of solutions of certain PDE dynamics through the
implementation of control functions, which are either supported on the
boundary of the domain on which the dynamics evolves, or locally
supported within said domain.
The objective of such controllability
or reachability problems would be the steering of the controlled PDE
solutions to a pre-assigned pro
file or state.