Input design via LMIs admitting frequency-Wise model specifications in confidence regions

IEEE Transactions on Automatic Control

Volumn 50, Issue 10, 2005, Pages 1534-1549

  Jansson, Henrik ^a   Hjalmarsson, Håkan ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Convex optimization; Input design; Robust control; System identification

Indexed keywords

IDENTIFICATION (CONTROL SYSTEMS); MATHEMATICAL MODELS; MATRIX ALGEBRA; OPTIMIZATION; PARAMETER ESTIMATION; ROBUSTNESS (CONTROL SYSTEMS);

CONVEX OPTIMIZATION; COVARIANCE MATRIX; INPUT DESIGN;

CONTROL SYSTEM SYNTHESIS;

EID: 27644436561     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2005.856652     Document Type: Article

References (56)

1. L. Ljung, System Identification-Theory for the User, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1999.
2. M. Campi, S. Ooi, and E. Weyer, "Non-asymptotic quality assessment of generalized FIR models with periodic inputs," Automatica, vol. 40, no. 12, pp. 2029-2041, 2004.
3. E. Weyer and M. Campi, "Global nonasymptotic confidence sets for general linear models," in Proc. 16th IFAC World Congr., Prague, Czech Republic, 2005.
4. Y. Zhu, Multivariable System Identification for Process Control. Oxford, U.K.: Pergamon, 2001.
5. G. Goodwin and R. Payne, Dynamic System Identification: Experiment Design and Data Analysis, Volume 136 of Mathematics in Science and Engineering. New York: Academic, 1977.
6. 2 input design in identification," in Proc. 16th IFAC World Congr., Prague, Czech Republic, 2005.
7. B. Ninness and H. Hjalmarsson, "Variance error quantifications that are exact for finite model order," IEEE Trans. Autom. Control, vol. 49, no. 8, pp. 1275-1291, Aug. 2004.
8. S. Bittanti, M. C. Campi, and S. Garatti, "New results on the asymptotic theory of system identification for the assessment of the quality of estimated models," in Proc. 41st IEEE Conf. Decision and Control, Las Vegas, NV, 2002.
9. S. Garatti, M. C. Campi, and S. Bittanti, "Model quality assessment for instrumental variable methods: Use of the asymptotic theory in practice," in Proc. 42nd IEEE Conf. Decision and Control, Maui, HI, 2003.
10. V.V. Fedorov, Theoryof Optimal Experiments, Volume 12 of Probability and Mathematical Statistics. New York: Academic, 1972.
11. R. K. Mehra, "Optimal input signals for parameter estimation in dynamic systems-Survey and new results," IEEE Trans. Autom. Control, vol. AC-19, no. 6, pp. 753-768, Jun. 1974.
12. M. Zarrop, Design for Dynamic System Identification, Lecture Notes in Control and Information Sciences. Sci. 21. Berlin, Germany: Springer-Verlag, 1979.
13. L. Ljung, "Asymptotic variance expressions for identified black-box transfer function models," IEEE Trans. Autom. Control, vol. AC-30, no. 9, pp. 834-844, Sep. 1985.
14. L. Ljung and Z. Yuan, "Asymptotic properties of black-box identification of transfer functions," IEEE Trans. Autom. Control, vol. AC-30, no. 6, pp. 514-530, Jun. 1985.
15. Z. Yuan and L. Ljung, "Unprejudiced optimal open loop input design for identification of transfer functions," Automatica, vol. 21, no. 6, pp. 697-708, 1985.
16. M. Gevers and L. Ljung, "Optimal experiment designs with respect to the intended model application," Automatica, vol. 22, no. 5, pp. 543-554, 1986.
17. H. Hjalmarsson, M. Gevers, and F. De Bruyne, "For model-based control design, closed loop identification gives better performance," Automatica, vol. 32, no. 12, pp. 1659-1673, 1996.
18. Y. C. Zhu and P. P. J. van den Bosch, "Optimal closed-loop identification test design for internal model control," Automatica, vol. 36, no. 8, pp. 1237-1241, 2000.
19. U. Forssell and L. Ljung, "Some results on optimal experiment design," Automatica, vol. 36, no. 5, pp. 749-756, May 2000.
20. Y. Zhu, "New development in industrial MPC identification," in Proc. AD-CHEM 2003, Int. Symp. Advanced Control of Chemical Processes, Hong Kong, China, Jan. 2004.
21. B. L. Cooley and J. H. Lee, "Control-relevant experiment design for multivariable systems described by expansions in orthonormal bases," Automatica, vol. 37, no. 2, pp. 273-281, 2001.
22. K. Lindqvist and H. Hjalmarsson, "Identification for control: Adaptive input design using convex optimization," in Proc. 40th IEEE Conf. Decision and Control, Orlando, FL, Dec. 2001.
23. J. H. Lee, "Control-relevant design of periodic test input signals for iterative open-loop identification of multivariable FIR systems," in Proc. 13th IFAC Symp. System Identification, Rotterdam, The Netherlands, 2003.
24. R. Hildebrand and M. Gevers, "Identification for control: Optimal input design with respect to a worst case ν-gap cost function," SIAM J. Control Optim., vol. 41, no. 5, pp. 1586-1608, 2003.
25. 2 input design for identification," in Proc. 43rd IEEE Conf. Decision and Control, Bahamas, 2004.
26. X. Bombois, G. Scorletti, M. Gevers, R. Hildebrand, and P. Van den Hof, "Least costly identification experiment for control," in MTNS'04, Leuven, Belgium, Jul. 2004.
27. X. Bombois, G. Scorletti, M. Gevers, R. Hildebrand, and P. Van den Hof, "Cheapest open-loop identification for control," in Proc. 43rd IEEE Conf. Decision and Control, Bahamas, 2004.
28. P. Stoica and T. Söderström, "A useful parameterization for optimal experiment design," IEEE Trans. Autom. Control, vol. AC-27, no. 4, pp. 986-989, Aug. 1982.
29. M. Gevers, X. Bombois, B. Codrons, G. Scorletti, and B. Anderson, "Model validation for control and controller validation in a prediction error identification framework - Part I:theory, Part II: applications," Automatica, vol. 39, no. 3, pp. 403-427, 2003.
30. X. Bombois, G. Scorletti, P. Van den Hof, and M. Gevers, "Least costly identification experiment for control. A solution based on a high-order model approximation," in Proc. Amer. Control Conference, Boston, MA, 2004.
31. S.-P. Wu, S. Boyd, and L. Vandenberghe, "FIR filter design via semidefinite programming and spectral factorization," in Proc. 35th IEEE Conf. Decision and Control, Kobe, Japan, 1996, pp.271-276.
32. V. A. Yakubovich, "Solution of certain matrix inequalities occurring in the theory of automatic control," Docl. Acad. Nauk. SSSR, pp. 1304-1307, 1962.
33. A. Rantzer, "On the Kalman-Yakubovich-Popov lemma," Syst. Control Lett., vol. 28, no. 1, pp. 7-10, 1996.
34. P. Stoica, T. McKelvey, and J. Mari, "MA estimation in polynomial time," IEEE Trans. Signal Process., vol. 48, pp. 1999-2012, 2000.
35. B. Wahlberg, "System identification using laguerre models," IEEE Trans. Autom. Control, vol. 36, no. 5, pp. 551-562, May 1991.
36. B. Wahlberg, "System identification using kautz models," IEEE Trans. Autom. Control, vol. AC-39, no. 6, pp. 1276-1281, Jun. 1994.
37. B. Ninness, H. Hjalmarsson, and F. Gustafsson, "The fundamental role of general orthonormal bases in system identification," IEEE Trans. Autom. Control, vol. 44, no. 7, pp. 1384-1406, Jul. 1999.
38. P. Heuberger, B. Wahlberg, and P. V. den Hof, Eds., Modeling and Identification with Rational Orthogonal Basis Functions. New York: Springer-Verlag, June 2005.
39. B. D. O. Anderson and J. Moore, Optimal Filtering. Upper Saddle River, NJ: Prentice-Hall, 1979.
40. K. Lindqvist, "On experiment design in identification of smooth linear systems," Licentiate thesis, 2001.
41. U. Grenander and G. Szegö, Toeplitz Forms and Their Applications. Berkley, CA: Univ. California Press, 1958.
42. C. Byrnes, S. Gusev, and A. Lindquist, "From finite covariance windows to modeling filters: A convex optimization approach," SIAM Rev., vol. 43, pp. 645-675, 2001.
43. I. Schur, "On power series which are bounded in the interior of the unit circle I and II," Reine Angew. Math., vol. 148, pp. 122-145, 1918.
44. B. Porat, Digital Processing of Random Signals. Upper Saddle River, NJ: Prentice-Hall, 1994.
45. P. Stoica and R. Moses, Introduction to Spectral Analysis. Upper Saddle River, NJ: Prentice-Hall, 1997.
46. R. Payne and G. Goodwin, "Simplification of frequency domain experiment design for SISO systems," Imperial College, London, U.K., Tech. Rep. 74/3, 1974.
47. H. Jansson, "Experiment design with applications in identification for control," Ph.D. thesis, Kungliga Tekniska Högskolan, Stockholm, Sweden, 2004.
48. M. Morari and E. Zafiriou, Robust Process Control. Upper Saddle River, NJ: Prentice-Hall, 1989.
49. K. Zhou, J. Doyle, and K. Glover, Robust and Optimal Control. Upper Saddle River, NJ: Prentice-Hall, 1996.
50. H. Hjalmarsson and H. Jansson, "Using a sufficient condition to analyze the interplay between identification and control," in Proc. 13th IFAC Symp. System Identification, Rotterdam, The Netherlands, 2003.
51. G. Vinnicombe, "Frequency domain uncertainty and the graph topology," IEEE Trans. Autom. Control, vol. 38, no. 9, pp. 1371-1383, Sep. 1993.
52. X. Bombois, M. Gevers, and G. Scorletti, "A measure of robust stability for an identified set of parametrized transfer functions," IEEE Trans. Autom. Control, vol. 45, no. 11, pp. 2141-2145, Nov. 2000.
53. X. Bombois, M. Gevers, G. Scorletti, and B. D. O. Anderson, "Robustness analysis tool for an uncertainty set obtained by prediction error identification," Automatica, vol. 37, no. 10, pp. 1629-1636, 2001.
54. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, Studies in Applied Applied Mathematics. Philadelphia, PA: SIAM, 1994.
55. ∞ state feedback with ellipsoidal parametric uncertainty," in Proc. 44th IEEE Conf. Decision and Control, Seville, Spain, Dec. 2005.
56. H. Jansson and H. Hjalmarsson, "Optimal experiment design in closed loop," in Proc. 16th IFAC World Congr., Prague, Czech Republic, 2005.