Model reduction based on modal Hankel singular values

In this paper, a model reduction for discrete-time singular dynamical systems is investigated. First, by transforming the original systems, the singular systems of impulse models are decomposed into the casual subsystems and the non-casual subsystems, and the reduction problem becomes merely a simplification of the non-casual subsystems reduction. Based on the Schur decomposition and apply Matlab to reorder the Schur forms, the degree of the systems state controllability and observability is scaled by Hankel singular values, and the results show that the controllability and observability of the states which are corresponding to the smaller Hankel singular values are weaker. Based on it, a new model reduction algorithm of discrete-time singular systems is given. Finally, a numerical simulation illustrates the effectiveness of the proposed algorithm.

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Truncated model reduction methods for linear time-invariant systems via eigenvalue computation

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331219899745 ◽

2020 ◽

Vol 42 (10) ◽

pp. 1908-1920

Author(s):

Ping Yang ◽

Yao-Lin Jiang

Keyword(s):

Model Reduction ◽

Newton Method ◽

Reduction Method ◽

Linear Time ◽

Singular Values ◽

Linear Time Invariant ◽

Hankel Singular Values ◽

Davidson Method ◽

Reduction Methods ◽

Linear Time Invariant Systems

This paper provides three model reduction methods for linear time-invariant systems in the view of the Riemannian Newton method and the Jacobi-Davidson method. First, the computation of Hankel singular values is converted into the linear eigenproblem by the similarity transformation. The Riemannian Newton method is used to establish the model reduction method. Besides, we introduce the Jacobi-Davidson method with the block version for the linear eigenproblem and present the corresponding model reduction method, which can be seen as an acceleration of the former method. Both the resulting reduced systems can be equivalent to the reduced system originating from a balancing transformation. Then, the computation of Hankel singular values is transformed into the generalized eigenproblem. The Jacobi-Davidson method is employed to establish the model reduction method, which can also lead to the reduced system equivalent to that resulting from a balancing transformation. This method can also be regarded as an acceleration of a Riemannian Newton method. Moreover, the application for model reduction of nonlinear systems with inhomogeneous conditions is also investigated.

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Analysis of multiplicity of Hankel singular values of control systems

Automation and Remote Control ◽

10.1134/s0005117915020022 ◽

2015 ◽

Vol 76 (2) ◽

pp. 205-218 ◽

Cited By ~ 2

Author(s):

L. A. Mironovskii ◽

T. N. Solov’eva

Keyword(s):

Control Systems ◽

Singular Values ◽

Hankel Singular Values

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Estimation of the Hankel Singular Values of Fractional-Order Systems

Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C ◽

10.1115/detc2009-87289 ◽

2009 ◽

Author(s):

Jay L. Adams ◽

Robert J. Veillette ◽

Tom T. Hartley

Keyword(s):

Fractional Order ◽

Dimensional Space ◽

Ritz Method ◽

Singular Values ◽

Finite Dimensional Space ◽

Fractional Order Systems ◽

Norm Estimates ◽

Finite Dimensional ◽

Hankel Singular Values ◽

Hankel Norm

This paper applies the Rayleigh-Ritz method to approximating the Hankel singular values of fractional-order systems. The algorithm is presented, and estimates of the first ten Hankel singular values of G(s) = 1/(sq+1) for several values of q ∈ (0, 1] are given. The estimates are computed by restricting the operator domain to a finite-dimensional space. The Hankel-norm estimates are found to be within 15% of the actual values for all q ∈ (0, 1].

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