scholarly journals Large-Scale Linear Systems from Order-Reduction

10.29007/xk7x ◽  
2018 ◽  
Author(s):  
Hoang-Dung Tran ◽  
Luan Viet Nguyen ◽  
Taylor T Johnson
Keyword(s):  
Linear Systems ◽  
Large Scale ◽  
Order Reduction ◽  
Single Mode ◽  
Hybrid Automaton ◽  
Model Order ◽  
Verification Tools ◽  
Test Sets ◽  
Benchmark Suite ◽  
And Robotics

This benchmark suite is composed of nine examples of large-scale linear systems, ranging in dimensionality in the tens to the low thousands. The benchmarks are derived from diverse fields such as civil engineering and robotics, and are based on similar existing test sets for model-order reduction algorithms in control and numerical analysis. Each example is provided in the SpaceEx XML model format as single-mode hybrid automaton and are compatible with the HyST model transformation tool to support analysis in other verification tools. Some preliminary reachability analysis results for some of the smaller examples (on the order of tens of dimensions) are presented using SpaceEx.

A Hybrid Approach for Model Order Reduction and Controller Design of Large-Scale Power Systems

2021 ◽  
pp. 211-226
Author(s):  
Rishabh Singhal ◽  
Yashonidhi Srivastava ◽  
Shini Agarwal ◽  
Abhimanyu Kumar ◽  
Souvik Ganguli
Keyword(s):  
Power Systems ◽  
Model Order Reduction ◽  
Large Scale ◽  
Controller Design ◽  
Hybrid Approach ◽  
Order Reduction ◽  
Model Order

scholarly journals Study of methods for dimension reduction of complex dynamic linear systems models

2018 ◽  
Vol 226 ◽  
pp. 04036
Author(s):  
Yuriy M. Manatskov ◽  
Torsten Bertram ◽  
Danil V. Shaykhutdinov ◽  
Nikolay I. Gorbatenko
Keyword(s):  
Linear Systems ◽  
Main Idea ◽  
Computation Time ◽  
Order Reduction ◽  
Complex Dynamic ◽  
Model Order ◽  
Reduced Order ◽  
Advantages And Disadvantages ◽  
Optimization Stage ◽  
Linear Systems Of Equations

Complex dynamic linear systems of equations are solved by numerical iterative methods, which need much computation and are timeconsuming ones, and the optimization stage requires repeated solution of these equation systems that increases the time on development. To shorten the computation time, various methods can be applied, among them preliminary (estimated) calculation or oversimple models calculation, however, while testing and optimizing the full model is used. Reduced order models are very popular in solving this problem. The main idea of a reduced order model is to find a simplified model that may reflect the required properties of the original model as accurately as possible. There are many methods for the model order reduction, which have their advantages and disadvantages. In this article, a method based on Krylov subspaces and SVD methods is considered. A numerical experiments is given.

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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