Title :
Iterative solution of operator Lyapunov equations arising in heat transfer
Author :
Reis, T. ; Wollner, Winnifried
Author_Institution :
Dept. of Math., Univ. of Hamburg, Hamburg, Germany
Abstract :
We consider an iterative method for the numerical solution of Lyapunov equations of infinite-dimensional control systems governed by an heat equation. Inspired by the `alternating direction implicit (ADI)´ iteration, which has been successfully applied to the solution of matrix Lyapunov equations, we present a method to determine approximations of the Gramian operator corresponding to the heat equation system. This method provides approximations of finite rank and is shown to be convergent in the nuclear norm.
Keywords :
Lyapunov matrix equations; heat transfer; iterative methods; multidimensional systems; ADI iteration; Gramian operator approximation; alternating direction implicit; finite rank approximations; heat equation system; heat transfer; infinite-dimensional control systems; iterative method; iterative solution; matrix Lyapunov equations; numerical solution; operator Lyapunov equations; Approximation methods; Boundary conditions; Equations; Generators; Heating; Hilbert space; Mathematical model;
Conference_Titel :
Control Conference (ECC), 2013 European
