Research Projects

Mathematical models are essential in understanding and analyzing control systems, often modeled by ordinary differential equations and algebraic constraints. However, sometimes these models can be transformed into ordinary differential equations (ODEs), which lack useful properties of the underlying physical phenomena. This project focuses on studying DAE systems in their most general form, which may be under-determined or over-determined. Control systems have three essential variables: input (control), output (measurable), and state (internal) variables. Estimating state variables is crucial for real-time information on the system. Functional observers, which estimate only a part or linear function of internal variables without estimating the whole vector of variables, are designed to estimate these variables in less computational time than standard full-state observers. The project aims to design filtering-based functional observers for DAE control systems with Gaussian and non-Gaussian noisy measurements, addressing the problem of noise contamination in state estimation. The Kalman filtering approach is a popular method for Gaussian noise estimation in standard linear state space systems.