Optimal L⁸ Model reduction using genetic algorithms

References

• Bultheel , A. and Barel , M. V. 1986 . “Padé Techniques for Model Reduction in Linear System Theory: A Survey” . Journal of Computational and Applied Mathematics , 14 : 401 – 438 .
   Web of Science ®Google Scholar
• Caponetto , R. , Fortuna , L. , Muscato , G. and Xibilia , M. G. 1996 . “Controller Reduction by Using Genetic Algorithms” . Journal of Systems Engineering , 6 : 113 – 118 .
   Google Scholar
• Fortuna , L. , Nunnari , G. and Gallo , A. 1992 . Model Order Reduction Techniques with Applications in Electrical Engineering , London : Springer‐Verlag .
   Google Scholar
• Glover , K. 1984 . “All Optimal Hankel‐norm Approximations of Linear Multivariable Systems and Their L8‐error Bounds” . International Journal of Control , 39 : 1115 – 1193 .
   Web of Science ®Google Scholar
• Goldberg , D. E. 1989 . Genetic Algorithm in Search, Optimization, and Machine Learning , Reading, MA : Addison‐Wesley .
   Google Scholar
• Guo , T. Y. and Hwang , C. 1996 . “Optimal Reduced‐order Models for Unstable and Nonmini‐mum‐phase Systems” . IEEE Trans. Circuits and Systems - I: Fundamental Theory and Applications , 43 ( 9 ) : 800 – 805 .
   Google Scholar
• Hutton , M. F. and Friedland , B. 1975 . “Routh Approximations for Reducing Order of Linear Time‐invariant Systems” . IEEE Transaction on Automatic Control , AC‐20 Jun. : 329 – 337 .
   Web of Science ®Google Scholar
• Hwang , C. and Guo , T. Y. 1985 . “Matrix Routh‐approximant Reduced‐order Modeling for Multivariable Systems” . International Journal of Systems Science , 16 : 697 – 712 .
   Web of Science ®Google Scholar
• Hwang , C. and Lee , Y. C. 1996 . “A New Family of Routh Approximants” . Circuits, Systems, and Signal Processing , 16 : 1 – 25 .
   Google Scholar
• Hwang , C. and Shieh , Y. P. 1982 . “Routh Approximation for Reducing Order of Discrete Systems” . Transactions of the ASME, Journal Dynamic Systems, Measurement, and Control , 104 : 107 – 109 .
   Web of Science ®Google Scholar
• Jury , E. I. 1982 . Inners and Stability of Dynamic Systems, , 2nd Ed. , New York : Krieger .
   Google Scholar
• Kavranoglu , D. and Bettayeb , M. 1993 . “Characterization of the Solution to the Optimal H8Approximation Problem” . Systems & Control Letters , 20 : 99 – 107 .
   Web of Science ®Google Scholar
• Kavranoglu , D. and Bettayeb , M. 1994 . “Characterization and Computation of the Solution to the Optimal L8 Approximation Problem” . IEEE Transactions on Automatic Control , 39 ( 9 ) : 1899 – 1904 .
   Google Scholar
• Krajewski , W. , Lepschy , A. and Viaro , U. 1993 . “Optimality Conditions in Multivariable L2Model Reduction” . Journal of the Franklin Institute , 330 : 431 – 439 .
   Google Scholar
• Lin , D. W. and Kung , S. Y. 1982 . “Optimal Hankel‐norm Approximation of Continuous‐time Linear Systems” . Circuits, Systems, and Signal Processing , 1 ( 3–4 ) : 407 – 431 .
   Google Scholar
• Man , K. F. , Tang , K. S. and Kwong , S. 1996 . “Genetic Algorithms: Concepts and Applications” . IEEE Transactions on Industrial Electronics , 43 : 519 – 534 .
   Web of Science ®Google Scholar
• Moore , B. C. 1981 . “Principal Component Analysis in Linear Systems: Controllability, Observability and Model Reduction” . IEEE Transactions on Automatic Control , 26 Feb. : 17 – 31 .
   Web of Science ®Google Scholar
• Nishioka , K. , Adachi , N. and Takeuchi , K. 1991 . “Simple Pivoting Algorithm for Root‐locus Method of Linear Systems with Delay” . International Journal of Control , 53 : 951 – 966 . 1991
   Web of Science ®Google Scholar
• Porter , B. 1968 . Stability Criteria for Linear Dynamical System , New York : Academic Press .
   Google Scholar
• Pujara , L. R. and Rattan , K. S. 1984 . “Model Reduction of Linear Multivariable Control Systems via Frequency Matching” . IEE Proceedings , 131 : 243 – 247 . Pt. D.
   Google Scholar
• Rao , A. S. , Lamba , S. S. and Rao , S. V. 1978 . “Routh‐approximant Time‐domain Reduced‐order Modeling for Single‐input, Single‐output Systems” . IEE Proceedings , 125 : 1059 – 1063 .
   Google Scholar
• Schelfhout , G. , Overschee , P. V. and Moor , B. D. 1994 . “Frequency weighted H2 model reduction” . In Nonlinear Numerical Methods and Rational Approximation II , Edited by: Cuyt , A. 287 – 199 . Dordrech : Kluwer Academic Publishers Group .
   Google Scholar
• Spanos , J. T. , Milman , M. H. and Mingori , D. L. 1992 . “A New Algorithm for L2 Optimal Model Reduction” . Automatica , 28 : 897 – 909 .
   Web of Science ®Google Scholar
• Srinvas , M. and Patnaik , L. M. 1994 . “Genetic Algorithms: A Survey” . Computer , 27 ( 6 ) : 17 – 26 .
   Google Scholar
• Therapos , C. P. 1989 . “Balancing Transformation for Unstable Nonminimal Linear Systems” . IEEE Transactions on Automatic Control , AC‐34 ( 4 ) Apr. : 455 – 457 .
   Google Scholar
• Zilouchian , A. 1991 . “Balanced Structures and Model Reduction of Unstable Systems” . Proc. of IEEE Southeastcon , 2 : 1198 – 1201 .
   Google Scholar
• Wilson , D. A. 1970 . “Optimal Solution of Model Reduction Problem” . IEE Proceedings , 117 : 1161 – 1165 .
   Web of Science ®Google Scholar
• Yamamoto , K. and Inoue , O. 1995 . “New Evolutionary Direction Operator for Genetic Algorithms” . AIAA Journal , 33 : 1990 – 1993 .
   Web of Science ®Google Scholar
• Yang , Z. J. , Hachino , T. and Tsuji , T. 1996 . “Model Reduction with Time Delay Combining the Least‐squares Method with the Genetic Algorithm” . IEE Proceedings‐Control Theory and Applications , 143 ( 3 ) : 247 – 254 .
   Google Scholar
• Correspondence addressee
   Google Scholar