Bounded-error uncertainty domain description for continuous-time state-space model

Author(s): W. Farah ; G. Mercère ; T. Poinot
DOI: 10.1049/iet-cta.2010.0725

For access to this article, please select a purchase option:

Buy article PDF

Buy Knowledge Pack

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership

Recommend Title Publication to library

IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

Author(s): W. Farah ¹ ; G. Mercère ¹ ; T. Poinot ¹
- Affiliations: 1: Laboratoire d'Automatique et Informatique Industrielle, University of Poitiers, Poitiers, France
Source: Volume 6, Issue 2, 19 January 2012, p. 261 – 273
DOI: 10.1049/iet-cta.2010.0725 , Print ISSN 1751-8644, Online ISSN 1751-8652

A method is introduced to determine the uncertainty domains of the estimated parameters for multi-input multi-output linear time-invariant continuous-time systems. This method uses a continuous-time subspace-based algorithm in order to identify the parameters of the system. This identification method is specific because the estimated state-space realisation is described with the help of a state-space canonical form. Then, a bounded-error approach is considered in order to characterise the uncertainty domains of the coefficients of the state-space matrices. A simulation example is included to demonstrate the efficiency of the developed method.

References

1. 1)
  - D. Bauer , M. Jansson . Analysis of the asymptotic properties of the MOESP type of subspace algorithms. Automatica , 497 - 509
2. 2)
  - Bako, L., Mercère, G., Lecoeuche, S.: `Identification of multivariable canonical state-space representations', Proc. IFAC Symp. on System Identification, July 2009, Saint Malo, France.
3. 3)
  - M. Matsubara , Y. Usui , S. Sugimoto . Identification of continuous-time MIMO systems via sampled data. Int. J. Innov. Comput. Inf. Control , 1119 - 1136
4. 4)
  - Tohme, E.: `Initialization of output error identification algorithms', 2008, PhD, Poitiers University, Poitiers, France.
5. 5)
  - G. Mercère , L. Bako . Parameterization and identification of multivariable statespace systems: a canonical approach. Automatica , 1547 - 1555
6. 6)
  - H. Garnier , L. Wang . (2008) Identification of continuous-time models from sampled data.
7. 7)
  - Ljung, L.: `Comments on model validation as set membership identification', Proc. Workshop on Robustness in Identification and Control, July 1999, Siena, Italy.
8. 8)
  - J. Munier , G.Y. Delistle . Spatial analysis using new properties of the cross-spectral matrix. IEEE Trans. Signal Process. , 3 , 746 - 749
9. 9)
  - M. Jansson , B. Wahlberg . On consistency of subspace methods for system identification. Automatica , 1507 - 1519
10. 10)
  - Viberg, M., Ottersten, B., Wahlberg, B., Ljung, L.: `A statistical perspective on state space modeling using subspace method', Proc. IEEE Conf. on Decision and Control, December 1991, Brighton, United Kingdom.
11. 11)
  - E. Walter , J. Norton , H. Piet-Lahanier , M. Milanese . (1996) Bounding approaches to system identification.
12. 12)
  - L. Giarré , M. Milanese , M. Taragna . H∞ identification and model quality evaluation. IEEE Trans. Autom. Control , 188 - 199
13. 13)
  - B. Ninness , G. Goodwin . Estimation of model quality. Automatica , 1771 - 1797
14. 14)
  - C. Baron , T. Poinot , J. Trigeassou . Determination of parametric uncertainty domains using least-squares technique and bounded errors. Meth. Models Autom. Control , 1003 - 1008
15. 15)
  - G. Mercère , M. Lovera . Convergence analysis of instrumental variable recursive subspace identification algorithms. Automatica , 1377 - 1386
16. 16)
  - M. Viberg . Subspace-based methods for the identification of linear time-invariant systems. Automatica , 1835 - 1851
17. 17)
  - M. Viberg , B. Wahlberg , B. Ottersten . Analysis of state space system identification methods based on instrumental variables and subspace fitting. Automatica , 1603 - 1616
18. 18)
  - Farah, W., Mercère, G., Poinot, T.: `System identification and uncertainty domain determination: a subspace-based approach', Proc. American Control Conf., June 2010, Baltimore, Maryland, USA.
19. 19)
  - Mercère, G., Ouvrard, R., Gilson, M., Garnier, H.: `Subspace-based methods for continuous-time model identification of MIMO systems from filtered sampled data', Proc. European Control Conf., July 2007, Kos, Greece.
20. 20)
  - G. Mercère , L. Bako , S. Lecoeuche . Propagator-based methods for recursive subspace model identification. Signal Process. , 468 - 491
21. 21)
  - A. Chiuso , G. Picci . The asymptotic variance of subspace estimates. J. Econom. , 257 - 291
22. 22)
  - R. Johansson . Identification of continuous-time models. IEEE Trans. Signal Process. , 887 - 897
23. 23)
  - J. Shao , D. Tu . (1995) The Jackknife and bootstrap.
24. 24)
  - T. Katayama . (2005) Subspace methods for system identification.
25. 25)
  - Haverkamp, B., Chou, C., Verhaegen, M., Johansson, R.: `Identification of continuous-time MIMO state space models from sampled data in the presence of process and measurement noise', Proc. IEEE Conf. on Decision and Control, December 1996, Kobe, Japan.
26. 26)
  - McKelvey, T.: `Identification of state space models from time and frequency data', 1995, PhD, Linköping University, Linköping, Sweden.
27. 27)
  - S. Bittanti , M. Lovera . Bootstrap-based estimates of uncertainty in subspace identification methods. Automatica , 1605 - 1615
28. 28)
  - M. Deistler , K. Peternell , W. Scherrer . Consistency and relative efficiency of subspace methods. Automatica , 1865 - 1875
29. 29)
  - A. Chiuso , G. Picci . Subspace identification by data orthogonalization and model decoupling. Automatica , 1689 - 1703
30. 30)
  - G. Belforte , B. Dona , V. Cerone . Parameter estimation algorithms for a set membership description of uncertainty. Automatica , 887 - 898
31. 31)
  - R. Johansson , M. Verhaegen , C.T. Chou . Stochastic theory of continuous-time state-space identification. IEEE Trans. Signal Process. , 1 , 41 - 51
32. 32)
  - P. Van Overschee , B. De Moor . Continuous-time frequency domain subspace system identification. Signal Process. , 2 , 179 - 194
33. 33)
  - Ljung, L.: `Model validation and model error modeling', Proc. Aström Symp. on Control, August 1999, Lund, Sweden.
34. 34)
  - Ljung, L.: `Identification model validation and control', Proc. IEEE Conf. on Decision and Control, December 1997, San Diego, California, USA.
35. 35)
  - H. Gariner , M. Mensler , A. Richard . Continuous-time model identification from sampled data: implementation issues and performance evaluation. Int. J. Control , 13 , 1337 - 1357
36. 36)
  - A. Ohsumi , K. Kameyama , K.I. Yamagushi . Subspace identification for continuous-time stochastic systems via distribution-based approach. Automatica , 1 , 63 - 79
37. 37)
  - Ramdani, N., Poignet, P.: `Experimental parallel robot dynamic model evaluation with set membership estimation', Proc. IFAC Symp. on System Identification, March 2006, Newcastle, Australia.
38. 38)
  - R. Horn , C. Johnson . (1985) Matrix analysis.
39. 39)
  - L. Giarré , M. Milanese . Model quality evaluation in H2 identification. IEEE Trans. Autom. Control , 691 - 698
40. 40)
  - Farah, W., Mercère, G., van Wingerden, J.W., Poinot, T.: `Quantification of model uncertainty for a state-space system', Proc. Int. Symp. on Mathematical Theory of Networks and Systems, July 2010, Budapest, Hungary.
41. 41)
  - A. Chiuso , G. Picci . Asymptotic variance of subspace methods by data orthogonalization and model decoupling: a comparative analysis. Automatica , 1705 - 1717
42. 42)
  - A. Chiuso . On the asymptotic properties of closed-loop CCA-type subspace algorithms: equivalence results and the role of the future horizon. IEEE Trans. Autom. Control , 634 - 649
43. 43)
  - T. Bastogne , H. Garnier , P. Sibille . A PMF-based subspace method for continuous-time model identification. Application to a multivariable winding process. Int. J. Control , 2 , 118 - 132
44. 44)
  - D. Bauer . Asymptotic properties of subspace estimators. Automatica , 359 - 376
45. 45)
  - A. Chiuso , G. Picci . Numerical conditioning and asymptotic variance of subspace estimates. Automatica , 677 - 683
46. 46)
  - K. Aström , P. Hagander , J. Sternby . Zeros of sampled systems. Automatica , 31 - 38
47. 47)
  - M. Moonen , B. De Moor , J. Vandewalle . (1991) SVD-based subspace methods for multivariable continuous-time systems identification.
48. 48)
  - M. Verhagen , V. Verdult . (2007) Filtering and system identification: a least squares approach.
49. 49)
  - L. Ljung . (1999) System identification. Theory for the user.
50. 50)
  - D. Bauer , M. Deistler , W. Scherrer . Consistency and asymptotic normality of some subspace algorithms for systems without observed inputs. Automatica , 1243 - 1254
51. 51)
  - Haverkamp, B.: `State space identification: theory and practice', 2001, PhD, Delft University of Technology, Delft, The Netherlands.
52. 52)
  - G. Goodwin , M. Gevers , B. Ninness . Quantifying the error in estimated transfer functions with application to model error selection. IEEE Trans. Autom. Control , 913 - 928
53. 53)
  - Ohta, Y., Kawai, T.: `Continuous-time subspace system identification using generalized orthonormal basis functions', Proc. Int. Symp. on Mathematical Theory of Networks and Systems, July 2004, Leuven, Belgium.
54. 54)
  - Huang, Y.-F., Gollamudi, S.: `Set-membership identification for adaptive equalization', Proc. Midwest Symp. on Circuits and Systems, August 1995, Rio de Janeiro, Brazil.
55. 55)
  - Bergamasco, M., Lovera, M.: `Continuous-time subspace identification in closed loop', Proc. 19th Int. Symp. on Mathematical Theory of Networks and Systems, July 2010, Budapest, Hungary.
56. 56)
  - P. Van Overschee , B. De Moor . (1996) Subspace identification for linear systems. Theory, implementation, applications.
57. 57)
  - Jansson, M.: `Asymptotic variance analysis of subspace identification methods', Proc. IFAC Symp. on System Identification, June 2000, Santa Barbara, California, USA.
58. 58)
  - de Vries, D.: `Identification of model uncertainty for control design', 1994, PhD, Delft University of Technology, Delft, The Netherlands.
59. 59)
  - McKelvey, T.: `Frequency domain system identification with instrumental variable based algorithm', Proc. Biennal Conf. on Mechanical Vibration and Noise, September 1997, Sacramento, Californian, USA.

Bounded-error uncertainty domain description for continuous-time state-space model

Bounded-error uncertainty domain description for continuous-time state-space model

Buy article PDF

Buy Knowledge Pack

Thank you

References

Related content