Description of Research

One major thrust of current research concerns implicit mathematical models. Depending on the area of application, such systems are called differential algebraic equations (DAEs), singular systems, descriptor systems, semi-state equations, constrained systems, or differential equations on a manifold. Usually the term DAE refers to systems of ordinary differential equations F(x', x, t)=0 with the Jacobian of F with respect to x' being singular. Many physical systems are most naturally and easily first modeled as an implicit system. This is often the case with computer generated models. A goal of our research is to be able to carry out analysis and simulation from the original implicit description thus reducing the time between formulation and numerical results. An implicit formulation also allows one to consider more complex phenomena and to explore different designs or parameter values from one model. We are interested in mathematical theory, numerical analysis and design of algorithms, and application.

Control applications are of special interest. This research currently includes both numerical approaches to optimal control problems and also problems in failure detection and failure identification

Among the topics being investigated are

There are always collaborations in progress with groups at other institutions. All of these collaborations have several different aspects not all of which are given here. Current collaborations are: