This minisymposium will focus on analytical and numerical techniques related to control and stabilization of large structures. Particular emphasis will be placed on flexible space structures (e.g. deformable mirrors, space radars, large antennas, manuverable robots) which by virtue of being "large and light" possess a very low degree of passive damping, and are therefore susceptible to the inducement of vibrations and difficult to control.
Most of the existing engineering algorithms designed to control/stabilize such structures are based on finite dimensional (ODE) models. As such, these algorithms do not account for the effects of high frequencies (high modes), critical for the overall stability of the structure. As a result, when applied to the real model, instabilities occur.
To cope with these difficulties, a different approach based on analysis of full PDE model has been recently developed. The resulting techniques involve very technical PDE estimates which, among other things, can predict apriori the ranges of effectiveness and the limitations related to the application of finite dimensional controls. Moreover, various numerical algorithms, based on discretization of PDE models, have been developed. Particularly interesting and mathematically challenging are problems involving boundary controls.
Organizer: Irena M. Lasiecka
University of Virginia