Automation and control have become an indispensable part of modern life. Using cruise control to set the speed of a car, landing a rover on Mars, or forecasting the weather, are all accomplished using tools from the field of automation and control systems theory. The successful development of automatic control algorithms requires a mathematical description of the relevant process. Most existing tools are limited in application to a specific kind of mathematical description, namely that of Ordinary Differential Equations (ODE) of finite order.
However, systems that are characterized by delays and transport phenomena, such as petroleum exploration and production and stability of large power transmission networks, requires a different kind of description known as infinite dimensional systems. To enable the effective use of automatic algorithms to these kinds of systems requires us to modify existing and develop new mathematical tools to handle the particular behavior of infinite dimensional systems. This will enable new, and enhance the existing, capabilities of monitoring, optimizing and controlling drilling and production processes, and provide tools and theory to deal with the stability of large distributed power system grids directly as infinite dimensional systems.
