Frequency-Domain Balanced Stochastic Truncation for Continuous and Discrete Time Systems

A new method for relative error continuous and discrete time model order reduction is proposed. The reduction technique is based on two recently developed methods, namely frequency domain balanced truncation within a frequency bound and inner-outer factorization techniques. The proposed method is of interest for practical model order reduction because in this context it shows to keep the accuracy of the approximation as high as possible without sacrificing the computational efficiency. Numerical results show the accuracy and efficiency enhancement of the method.

[1]  Ali Zilouchian,et al.  Model reduction of large scaled systems via frequency-domain balanced structures , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[2]  Sung Jin Yoo,et al.  Output Feedback Dynamic Surface Control of Flexible-Joint Robots , 2008 .

[3]  Byoung-Ho Kim.  An Interphalangeal Coordination-based Joint Motion Planning for Humanoid Fingers: Experimental Verification , 2008 .

[4]  Ali Zilouchian,et al.  Model reduction of large-scale systems using perturbed frequency domain balanced structure , 2003 .

[5]  Ali Zilouchian,et al.  Principle of frequency-domain balanced structure in linear systems and model reduction , 2003, Comput. Electr. Eng..

[6]  Paul Van Dooren,et al.  Model Reduction of Large-Scale Dynamical Systems , 2004, International Conference on Computational Science.

[7]  András Varga,et al.  Computation of general inner-outer and spectral factorizations , 2000, IEEE Trans. Autom. Control..

[8]  A. Zilouchian,et al.  Controller order reduction of large-scale plants using preferred frequency weighted functions , 2002, Proceedings of the 5th Biannual World Automation Congress.

[9]  A. Varga,et al.  On stochastic balancing related model reduction , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[10]  M. Green,et al.  A relative error bound for balanced stochastic truncation , 1988 .

[11]  A. Antoulas,et al.  A Survey of Model Reduction by Balanced Truncation and Some New Results , 2004 .

[12]  Michael Green,et al.  Balanced stochastic realizations , 1988 .

[13]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[14]  H.R. Shaker,et al.  Accuracy enhancement in HiMAT aircraft controller reduction , 2006, 2006 1st International Symposium on Systems and Control in Aerospace and Astronautics.

[15]  A. Varga,et al.  The general inner-outer factorization problem for discrete-time systems , 1999, 1999 European Control Conference (ECC).

[16]  B. Moore.  Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[17]  U. Desai,et al.  A transformation approach to stochastic model reduction , 1984 .

[18]  A. Zilouchian,et al.  Controller Order Reduction Using the Neighborhood of Crossover Frequency Approach , 2004 .