My name is Xingang Cao and I researching model order reduction for parameter-varying systems at the Centre for Analysis, Scientific computing and Applications (CASA) in the Department of Mathematics and Computer Science. The aim of my research is to achieve system reduction by minimizing the distance between the full-order model and the reduced-order model.
Solving the model reduction conundrum
There are three key challenges my research addresses, the first of which is that coupling the time-varying parameter and the system states makes it impossible to derive the transfer function (matrix). So methods based on the transfer function cannot be applied anymore. Secondly, linear parameter-varying (LPV) systems are actually linear time-varying (LTV) systems but since the parameter trajectory cannot be known in advance, this makes the time-varying analysis more difficult. Finally, the projection matrices are functions of parameters, which means that we have to work in non-Euclidean spaces to find those functions. What I have done, therefore, is to assume that the parameter trajectory is known and then propose a Riemannian conjugate gradient method to solve the norm model reduction problem.
Shorter, cheaper development cycles
I think that the researchers or the companies who work on MEMS, supersonic (aero) vehicles and high-precision systems will be interested in my research. LPV systems always pop up in these areas and the original models are usually obtained from large-scale finite element analysis. Hence, model order reduction technique is required so that optimal design, fast simulation and model-based (real-time) control can be enabled. My research will therefore enable fast and efficient simulation of complex physical systems so that a new generation of computer-aided design (CAD) and engineering (CAE) can be produced. As a result, development cycles of new processes and products can be shorter and cheaper.