Krylov-subspace methods for reduced-order modeling in circuit simulation
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Krylov subspace methods for large-scale matrix problems in control
Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
Using adaptive proper orthogonal decomposition to solve the reaction--diffusion equation
Applied Numerical Mathematics
A control law for a nonlinear heat conduction problem on nontrivial domains using FEM
MED '09 Proceedings of the 2009 17th Mediterranean Conference on Control and Automation
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The mathematical models for dynamic distributed parameter systems are given by systems of partial differential equations. With nonlinear material properties, the corresponding finite element (FE) models are large systems of nonlinear ordinary differential equations. However, in most cases, the actual dynamics of interest involve only a few of the variables, for which model reduction strategies based on system theoretical concepts can be immensely useful. This paper considers the problem of controlling a three dimensional profile on nontrivial geometries. Dynamic model is obtained by discretizing the domain using FE method. A nonlinear control law is proposed which transfers any arbitrary initial temperature profile to another arbitrary desired one. The large dynamic model is reduced using proper orthogonal decomposition (POD). Finally, the stability of the control law is proved through Lyapunov analysis. Results of numerical implementation are presented and possible further extensions are identified.