PDE methods for infinite-dimensional systems

Organisers: George Avalos, Richard Rebarber (Lincoln - Nebraska)

In the study of the control theory of partial differential equations, the first issues to be addressed are the existence, uniqueness and regularity of controlled solutions. These are nontrivial even for linear systems, since for the purposes of control theory it is important to obtain solutions in the space of maximum regularity. For most systems the classical questions of controllability, observability, stabilizability, detectability, and optimal control are especially challenging, requiring both PDE techniques and control theory techniques. In this session we will address these questions, with an emphasis on two important areas in which there has recently been a great deal of progress, nonlinear systems and coupled systems. Nonlinearities occur naturally in most systems, and often cannot be ignored for the purposes of effective control. The study of coupled systems is a natural step towards understanding how to control complex structures. We also address some systems theoretical design issues for coupled systems, and also the issue of shape optimization.

Richard Rebarber: Generalized Hold Sampled Data Design for PDEs

Walter Littman: Robustness of the "SUR" method of boundary control (smoothness + uniqueness + reversibility implies controllability) under small bounded perturbation of the coefficients

Scott Hansen (Iowa State): Exact controllability of multilayer beams and plates

Jan Sokolowski: Applications of self adjoint extensions of elliptic operators to defect modelling

George Avalos (Nebraska)

Kirsten Morris, Waterloo: Feedback in the Disturbance Decoupling Problem for Infinite-Dimensional Systems

Marius Tucsnak: The numerical viscosity method for the approximation of infinite dimensional LQR problems

Written by Stuart Townley
Last modified: January 2003