scholarly journals Balanced model order reduction for linear random dynamical systems driven by Lévy noise

2018 ◽  
Vol 0 (0) ◽  
pp. 1-27
Author(s):  
Martin Redmann ◽  
◽  
Melina A. Freitag ◽  
Keyword(s):  
Dynamical Systems ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Random Dynamical Systems ◽  
Lévy Noise ◽  
Model Order ◽  
Balanced Model ◽  
Levy Noise

Singular perturbation approximation for linear systems with Lévy noise

2018 ◽  
Vol 18 (04) ◽  
pp. 1850033 ◽  
Author(s):  
Martin Redmann ◽  
Peter Benner
Keyword(s):  
Singular Perturbation ◽  
Linear Systems ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Reduction Technique ◽  
Lévy Noise ◽  
Model Order ◽  
Linear Evolution Equation ◽  
Levy Noise ◽  
Perturbation Approximation

To solve a stochastic linear evolution equation numerically, finite dimensional approximations are commonly used. For a good approximation, one might end up with a sequence of ordinary stochastic linear equations of high order. To reduce the high dimension for practical computations, we consider the singular perturbation approximation as a model order reduction technique in this paper. This approach is well-known from deterministic control theory and here we generalize it for controlled linear systems with Lévy noise. Additionally, we discuss properties of the reduced order model, provide an error bound, and give some examples to demonstrate the quality of this model order reduction technique.

Using model order reduction to accelerate optimization of multi-stage linear dynamical systems

2014 ◽  
pp. 453-458
Author(s):  
Yao Yue ◽  
Suzhou Li ◽  
Lihong Feng ◽  
Andreas Seidel-Morgenstern ◽  
Peter Benner
Keyword(s):  
Dynamical Systems ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Model Order ◽  
Linear Dynamical Systems ◽  
Multi Stage

scholarly journals AN ITERATIVE MODEL ORDER REDUCTION METHOD FOR LARGE-SCALE DYNAMICAL SYSTEMS

2017 ◽  
Vol 59 (1) ◽  
pp. 115-133
Author(s):  
K. MOHAMED ◽  
A. MEHDI ◽  
M. ABDELKADER
Keyword(s):  
Dynamical Systems ◽  
Model Order Reduction ◽  
Large Scale ◽  
Reduction Method ◽  
Linear Time ◽  
Order Reduction ◽  
Lyapunov Equation ◽  
Model Order ◽  
Iterative Model ◽  
Order Reduction Method

We present a new iterative model order reduction method for large-scale linear time-invariant dynamical systems, based on a combined singular value decomposition–adaptive-order rational Arnoldi (SVD-AORA) approach. This method is an extension of the SVD-rational Krylov method. It is based on two-sided projections: the SVD side depends on the observability Gramian by the resolution of the Lyapunov equation, and the Krylov side is generated by the adaptive-order rational Arnoldi based on moment matching. The use of the SVD provides stability for the reduced system, and the use of the AORA method provides numerical efficiency and a relative lower computation complexity. The reduced model obtained is asymptotically stable and minimizes the error ($H_{2}$and$H_{\infty }$) between the original and the reduced system. Two examples are given to study the performance of the proposed approach.

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