Controller Reduction: Concepts and Approaches

IEEE Transactions on Automatic Control

Volumn 34, Issue 8, 1989, Pages 802-812

  Anderson, Brian D O ^a   Liu, Yi ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES--APPROXIMATION THEORY; SYSTEM STABILITY;

CONTROLLER REDUCTION; COPRIME FACTORIZATION; FRACTIONAL CONTROLLER REPRESENTATION; FREQUENCY WEIGHTING; HANKEL NORM APPROXIMATION;

CONTROL SYSTEMS, LINEAR;

EID: 0024716281     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/9.29422     Document Type: Article

References (37)

1. D. Gangsaas K.R. Bruce J.D. Blight U.L Ly “Application of modern synthesis to aircraft control: Three case studies” IEEE Trans. Automat. Contr vol.Ac-31 pp.995-1104 Nov 1986
2. U.L. Ly, “A design algorithm for robust low order controller,” Ph.D. dissertation, Dep. Aeronaut. Astronaut., Stanford Univ., Stanford, CA, 1982.
3. D. S. Bernstein and D. C. Hyland, “The optimal projection equations for fixed-order dynamic compensation,” IEEE Trans. Automat. Contr., vol. AC-29, pp. 1034–1037, Nov. 1985.
4. D. C. Hyland and D. S. Bernstein, “The optimal projection equations for model reduction and the relationships among the methods of Wilson, Skelton, and Moore,” IEEE Trans. Automat. Contr., vol. AC-30, pp. 1201–1211, Dec. 1985.
5. D. S. Bernstein and D. C. Hyland, “Optimal projection/maximum entropy stochastic modeling and reduced-order design synthesis,” in Proc. IFAC Workshop on Model Errors and Compensation, Boston, MA, 1985.
6. S. W. Greeley and D. C. Hyland, “Reduced order compensation: LQG reduction versus optimal projection using a homotopic continuation method, ” in Proc. 26th IEEE Conf. Decision Contr., Los Angeles, CA, 1987, pp. 742–747.
7. R. E. Skelton, Dynamic Systems Control. New York: Wiley, 1988.
8. E. A. Jonckheere and L. M. Silverman, “Singular value analysis deformable systems,” in Proc. 20th IEEE Conf. Decision Contr., Los Angeles, CA, 1981.
9. D. Enns, “Model reduction for control systems design,” Ph.D. dissertation, Dep. Aeronaut. Astronaut., Stanford Univ., Stanford, CA, 1984.
10. J. C. Doyle and G. Stein, “Multivariable feedback design: Concepts for a classical/modern synthesis,” IEEE Trans. Automat. Contr., vol. AC-26, no. 1, pp. 4–16, 1981.
11. B. C. Moore, “Principal component analysis in linear systems: Controllability, observability, and model reduction,” IEEE Trans. Automat. Contr., vol. AC-26, no. 1, pp. 17–32, 1982.
12. L. Pernebo and L. M. Silverman, “Modern reduction via state space representations,” IEEE Trans. Automat. Contr., vol. AC-27, no. 2, pp. 382–387, 1982.
13. V. M. Adamjan, D. Z. Arov, and M. G. Krein, “Analytic properties of Schmidt pairs for Hankel operator and the generalized Schur-Takagi problem,” Math. USSR Sbornik, vol. 15, no. 1, pp. 31–73, 1971.
14. S. Y. Rung and D. W. Lin, “Optimal Hankel-norm model reductions: Multivariable systems,” IEEE Trans. Automat. Contr., vol. AC-26, no. 4, pp. 832–852, 1981.
15. K. Glover and D. J. N. Limebeer, “Robust system design using optimal reduced order plant methods,” in Proc. ACC, San Francisco, CA, 1983, p. 664.
16. K. Glover, “All optimal Hankel-norm approximations of linear multivariable systems and their L∞ error bounds,” Int. J. Contr., vol. 39, no. 6, pp. 1115–1193, 1984.
17. A. Yousuff, D. A. Wagie, and R. E. Skelton, “Linear system approximation via covariance equivalent realizations,” J. Math. Anal. Appl., vol. 106, no. 1, pp. 91–115, 1985.
18. A. Yousuff and R. E. Skelton, “Covariance equivalent realizations with application to model reduction of large-scale systems,” Contr. Dynam. Syst., vol. 22, pp. 273–348, 1985.
19. B. D. O. Anderson and R. E. Skelton, “The generation q-Markov covers,” IEEE Trans. Circuits Syst., vol. CAS-35, no. 4, pp. 375–384, 1988.
20. A. Yousuff and R. E. Skelton, “Controller reduction by component cost analysis,” IEEE Trans. Automat. Contr., vol. AC-29, no. 6, 520–530, 1984.
21. G. A. Latham and B. D. O. Anderson, “Frequency-weighted optimal Hankel norm approximation of stable transfer functions,” Syst. Contr. Lett., vol. 5, no. 4, pp. 229–236, 1985.
22. B. D. O. Anderson, “Weighted Hankel norm approximation: Calculation of bounds,” Syst. Contr. Lett., vol. 7, no. 4, pp. 247–255, 1986.
23. R. E. Skelton and B. D. O. Anderson, “Weighted q-Markov covers,” submitted for publication.
24. D. F. Enns, “Model reduction with balanced realizations: An error bound and a frequency weighted generalization,” in Proc. 23rd Conf. Decision Contr., Las Vegas, NV, 1984, pp. 127–132.
25. E. A. Jonckheere and L. M. Silverman, “A new set of invariants for linear systems—Application and approximation,” presented at the Int. Symp. Theory Networks & Syst., Santa Monica, CA, 1981.
26. A. Yousuff and R. E. Skelton, “A note on balanced controller reduction,” IEEE Trans. Automat. Contr., vol. AC-29, no. 3, pp. 254–257, 1984.
27. E. J. Verriest, “Suboptimal LQG design via balanced realizations,” in Proc. 20th IEEE Conf. Decision Contr., San Diego, CA, 1981, pp. 686–687.
28. J. A. Davis and R. E. Skelton, “Another balanced controller reduction algorithm,” Syst. Contr. Lett., vol. 4, no. 2, pp. 79–83, 1984.
29. P. J. Parker and B. D. O. Anderson, “Unstable rational function approximation,” Int. J. Contr., vol. 46, no. 5, pp. 1783–1801, 1987.
30. C. N. Nett, C. A. Jacobson, and M. J. Balas. “A connection between state-space and doubly coprime fractional representations,” IEEE Trans. Automat. Contr., vol. AC-29, no. 9, pp. 831–832, 1984.
31. M. Vidyasagar, Control System Synthesis: A Factorization Approach. Cambridge, MA: M.I.T. Press, 1985.
32. Y. Liu and B. D. O. Anderson, “Controller reduction via stable factorization and balancing,” Int. J. Contr., vol. 44, no. 2, pp. 507–531, 1986.
33. Y. Liu, B. D. O. Anderson, and U.L. Ly, “Coprime factorization controller reductions with Bezout identity induced frequency weighting,” submitted for publication.
34. C. de Villemagne and R. E. Skelton, “Controller reduction using canonical interactions,” IEEE Trans. Automat. Contr., vol. 33, pp. 740–750, Aug. 1988.
35. Y. Liu and B. D. O. Anderson, “Frequency weighted controller reduction methods and loop transfer recovery,” submitted for publication.
36. K. Glover, “Multiplicative approximation of linear multivariable systems with L∞ error bounds,” in Proc. ACC, Seattle, WA, 1986, pp. 1705–1709.
37. J. P. Keller and D. Bonvin, “Selection of inputs for the purpose of model reduction and control design,” in Proc. 10th IFAC World Congress, Munich, 1987, vol. 2, pp. 226–231.