Computational Issues in Control and Design: From Ultra Small Nano-Devices to Ultra Large Space Structures

John A. Burns

Interdisciplinary Center for Applied Mathematics

Virginia Polytechnic Institute and State University

Blacksburg, VA 24061-0531, USA

In this talk we discuss mathematical and computational issues concerning the development of mathematical tools for design, control and optimization of systems governed by partial-integro differential equations. We present two applications to motivate the talk and to illustrate how distributed parameter control theory can be used to address some theoretical and computational difficulties. Both applications involve systems where the material properties must be considered. The first problem involves the modeling and control of thin film growth and is an important component of manufacturing nano-scale devices. We focus on a phenomenological model for epitaxial growth of thin films described by a nonlinear continuum model that accounts for kinetic roughening and coarsening in film growth. The second problem involves modeling and control of large inflatable space structures. Inflatable and rigidizable space structures have been the subject numerous scientific studies for the past fifty years and considerable progress has been made in the development of new materials and technologies for the design and manufacturing of these structures. However, modeling and control of these structures remains a challenging problem. We discuss these problems and present some preliminary results.