Reduced order modeling and robust controller design for a heat conduction problem

This paper considers the problem of modeling of a two-dimensional problem of heating of a nontrivial geometry. The system is described by Partial Differential Equations and a large no. of Ordinary Differential Equations are obtained through Finite Element method. The ODE model is reduced using SVD-Krylov decomposition technique. Finally a robust controller is designed which transfers the temperatures from any initial profile to a desired one. Results of the numerical implementations are presented and possible further extensions are identified.