scholarly journals The Versatile Cross Gramian for System Theoretic Model Reduction and More

2015 ◽  
Author(s):  
Christian Himpe ◽  
Mario Ohlberger
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Theoretic Model ◽  
Model Order ◽  
Gramian Matrix ◽  
The Cross ◽  
Analysis System ◽  
Single Matrix ◽  
Controllability And Observability ◽  
Symmetric Systems

For input-output systems, the cross gramian matrix encodes controllability and observability information into a single matrix, which are essential to system-theoretic applications. This system gramian can be used, in example, for model order reduction, sensitivity analysis, system identification, decentralized control and parameter identification. Beyond linear symmetric systems, the cross gramian is also available for parametric, non-symmetric, non-square and nonlinear systems.

scholarly journals Reduced Order Controller Design for Symmetric, Non-Symmetric and Unstable Systems Using Extended Cross-Gramian

Machines ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 48 ◽  
Author(s):  
Azhar ◽  
Zulfiqar ◽  
Liaquat ◽  
Kumar
Keyword(s):  
Model Order Reduction ◽  
Controller Design ◽  
Order Reduction ◽  
Original System ◽  
Computational Effort ◽  
Model Order ◽  
Unstable Systems ◽  
Reduced Order ◽  
The Cross ◽  
Symmetric Systems

In model order reduction and system theory, the cross-gramian is widely applicable. The cross-gramian based model order reduction techniques have the advantage over conventional balanced truncation that it is computationally less complex, while providing a unique relationship with the Hankel singular values of the original system at the same time. This basic property of cross-gramian holds true for all symmetric systems. However, for non-square and non-symmetric dynamical systems, the standard cross-gramian does not satisfy this property. Hence, alternate approaches need to be developed for its evaluation. In this paper, a generalized frequency-weighted cross-gramian-based controller reduction algorithm is presented, which is applicable to both symmetric and non-symmetric systems. The proposed algorithm is also applicable to unstable systems even if they have poles of opposite polarities and equal magnitudes. The proposed technique produces an accurate approximation of the reduced order model in the desired frequency region with a reduced computational effort. A lower order controller can be designed using the proposed technique, which ensures closed-loop stability and performance with the original full order plant. Numerical examples provide evidence of the efficacy of the proposed technique.

scholarly journals System‐theoretic model order reduction with pyMOR

PAMM ◽  
2019 ◽  
Vol 19 (1) ◽  
Author(s):  
Linus Balicki ◽  
Petar Mlinarić ◽  
Stephan Rave ◽  
Jens Saak
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Theoretic Model ◽  
Model Order
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