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Several generalized state-space models arising from a semi-discretization of a controlled heat transfer process for optimal cooling of steel profiles are presented. The model orders differ due to different levels of refinement applied to the computational mesh. 1 The model equations We consider the problem of optimal cooling of steel profiles. This problem(More)
in accordance with the requirements for the degree Dr. rer. nat. M ˙ x(t)= N x(t)+ B u(t); y(t)= C x(t) ˆ M ˙ ˆ x(t) = ˆ N ˆ x(t)+ ˆ B u(t); y(t)= ˆ C ˆ x(t) ii iii to S ¸enay iv ACKNOWLEDGEMENTS Financial Support. Large parts of this research have been refined in the projects Parallele numerische Lösung von Optimalsteuerungsproblemen f ¨ ur instationäre(More)
Efficient numerical algorithms for the solution of large and sparse matrix Riccati and Lyapunov equations based on the low rank alternating directions implicit (ADI) iteration have become available around the year 2000. Over the decade that passed since then, additional methods based on extended and rational Krylov subspace projection have entered the field(More)
The numerical treatment of linear-quadratic regulator problems for parabolic partial differential equations (PDEs) on infinite time horizons requires the solution of large scale algebraic Riccati equations (ARE). The Newton-ADI iteration is an efficient numerical method for this task. It includes the solution of a Lyapunov equation by the alternating(More)
Low-rank versions of the alternating direction implicit (ADI) iteration are popular and well established methods for the numerical solution of large-scale Sylvester and Lyapunov equations. Probably the largest disadvantage of these methods is their dependence on a set of shift parameters that are crucial for a fast convergence. Here we compare existing(More)
Model order reduction of large-scale linear time-invariant systems is an omnipresent task in control and simulation of complex dynamical processes. The solution of large scale Lyapunov and Riccati equations is a major task, e.g., in balanced truncation and related model order reduction methods, in particular when applied to semi-discretized partial(More)
Linearizing constraint equations of motion around equilibrium points in mechanics or coupling electrical and mechanical parts in mechatronics one obtains large sparse second-order index-1 differential algebraic (DAE) models. To get reduced order models of such systems, first they can be rewritten into first-order models. Then, model reduction techniques are(More)
The solution of large-scale Lyapunov equations is a crucial problem for several fields of modern applied mathematics. The low-rank Cholesky factor version of the alternating directions implicit method (LRCF-ADI) is one iterative algorithm that computes approximate low-rank factors of the solution. In order to achieve fast convergence it requires adequate(More)