作者：
Jens BremerJan HeilandPeter BennerKai SundmacherMax Planck Institute Magdeburg
Dpt. Process Systems Engineering Sandtorstraße 2 39106 Magdeburg Germany and Otto von Guericke University Magdeburg Chair for Process Systems Engineering Universitätsplatz 2 39106 Magdeburg (Sundmacher) Max Planck Institute Magdeburg
Dpt. Computational Methods in Systems and Control Theory and Otto von Guericke University Magdeburg Fakultät für Mathematik
The optimization of a controlled process in a simulation without access to the model itself is a common scenario and very relevant to many chemical engineering applications. A general approach is to apply a black-box ...
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The optimization of a controlled process in a simulation without access to the model itself is a common scenario and very relevant to many chemical engineering applications. A general approach is to apply a black-box optimization algorithm to a parameterized control scheme. The success then depends on the quality of the parametrization that should be low-dimensional though rich enough to express the salient features. This work proposes using solution snapshots to extract dominant modes of the temporal dynamics of a process and use them for low-dimensional parametrizations of control functions. The approach is called proper orthogonal decomposition in time (time-POD). We provide theoretical reasoning and illustrate the performance for the optimal control of a methanation reactor.
This paper aims at the efficient numerical solution of stochastic eigenvalue problems. Such problems often lead to prohibitively high dimensional systems with tensor product structure when discretized with the stochas...
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An increasing amount of collected data are high-dimensional multi-way arrays (tensors), and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible. The ever present cur...
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In this note, we consider the existence and uniqueness of the solution of a time-dependent optimal control problem constrained by a partial differential equation with uncertain inputs. Relying on the Lions’ Lemma for...
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Free boundary and moving boundary problems, that can be used to model crystal growth or the solidification and melting of pure materials, receive growing attention in science and technology. The optimal control of the...
We propose a new implementation of the sign function based spectral divide-and-conquer method for the generalized non-symmetric eigenvalue problem. The basic idea is to use the generalized matrix sign function to spli...
Based on our recent findings [1, 2] regarding the low-rank ADI iteration for large-scale Lyapunov equations, we propose a mathematically equivalent formulation of the LR-ADI whose iteration is directly connected to lo...
We present a new reformulation of the low-rank ADI method for solving large-scale Lyapunov equations which uses only real arithmetic operation and storage in the presence of complex shift parameters. This makes the me...
The differential Riccati equation appears in different fields of applied mathematics like controltheory and systemstheory. For large-scale systems the numerical solution comes with a large amount of storage requirem...
The differential Riccati equation appears in different fields of applied mathematics like controltheory and systemstheory. For large-scale systems the numerical solution comes with a large amount of storage requirements. This motivates the use of Krylov subspace and projection based methods [1–3]. In the present paper we apply an invariance theorem for ODEs to the differential Riccati Equation. We show that the solution is contained in a Krylov like subspace and extend our results to certain time-varying cases.
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