Spatial-Temporal Systems and Model Reduction

Many dynamical phenomena evolve both in space and time. We refer to these systems as spatial-temporal systems and their study is usually of a more difficult nature than systems that evolve over time only. Examples  of these systems include electromagnetic behavior in materials such as transformers, sensors and actuation systems, flow phenomena in fluids and gasses, and thermodynamical aspects in materials and devices. 

The behavior of such systems is typically described by partial differential equations and the analysis of these models is usually difficult. In the control systems group we study and model these classes of system for purposes such as simulation, analysis and control system design. Because of the difficult mathematical nature of these systems, we study methods to reduce the complexity of these systems. We develop tools for model approximation that allow fast and accurate simulation of such models. Also, we develop modeling tools for specific classes of spatial-temporal systems that allow an efficient synthesis of controllers and detailed analysis of system properties.