NDLI: Structure preserving balanced proper orthogonal decomposition for second-order form systems via shifted Legendre polynomials

Content Provider	IET Digital Library
Author	Xiao, Zhi Hua Jiang, Yao Lin Qi, Zhen Zhong
Abstract	This study considers structure preserving balanced proper orthogonal decomposition for second-order form systems via shifted Legendre polynomials. The proposed approach is to use time interval empirical Gramians of the first-order representation, which are constructed from impulse responses by solving block tridiagonal linear systems, to generate approximate balanced system for the large-scale second-order form system. The balancing transformation is directly computed from the expansion coefficients of impulse responses in the space spanned by shifted Legendre polynomials, without computing the full Gramians for the first-order representation. Then, the reduced second-order model is constructed by truncating the states corresponding to the small approximate singular values. Furthermore, in combination with the dominant subspace projection method, the authors modify the reduction procedure to alleviate the shortcoming of the above method, which may unexpectedly lead to unstable systems even though the original one is stable. The stability preservation of the reduced model is briefly discussed. Finally, the effectiveness of the proposed methods is demonstrated by two numerical experiments.
Starting Page	1155
Ending Page	1165
Page Count	11
ISSN	17518644
Volume Number	13
e-ISSN	17518652
Issue Number	Issue 8, May (2019)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-cta/13/8
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-cta.2018.5946
Journal	IET Control Theory & Applications
Publisher Date	2019-03-25
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Algebra Approximate Balanced System Balanced Proper Orthogonal Decomposition Balancing Transformation Block Tridiagonal Linear System Control System Analysis First-order Representation Graph Theory Impulse Responses Interpolation And Function Approximation Legendre Polynomials Linear Algebra Linear System Matrix Algebra Numerical Analysis Numerical Approximation And Analysis Parallel Algorithm Reduced Order System Second-order Form System Second-order Model Set Theory Shifted Legendre Polynomials Statistics Synthesis Method Time Interval Empirical Gramians Unstable System
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Human-Computer Interaction Electrical and Electronic Engineering Computer Science Applications

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