Set-membership EIV identification through LMI relaxation techniques

Proceedings of the 2010 American Control Conference, ACC 2010

Volumn , Issue , 2010, Pages 2158-2163

  Cerone, V ^a   Piga, D ^a   Regruto, D ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Errors invariables; LMI relaxation; Set membership identification

Indexed keywords

CONVEX OPTIMIZATION; LINEAR CONTROL SYSTEMS;

ALGEBRAIC OPTIMIZATION; CONVERGENCE PROPERTIES; ERROR IN VARIABLE (EIV); IDENTIFICATION PROBLEM; LINEAR DYNAMIC SYSTEM; LMI RELAXATION; PARAMETERS UNCERTAINTIES; SET-MEMBERSHIP IDENTIFICATION;

LINEAR MATRIX INEQUALITIES;

EID: 77957814272     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/acc.2010.5531327     Document Type: Conference Paper

References (25)

1. L. Ljung, System Identification, Theory for the User. Upper Saddle River: Prentince Hall, 1999.
2. T. Söderström and P. Stoica, System Identification. Upper Saddle River: Prentice Hall, 1989.
3. M. Verhaegen and V. Verdult, Filtering and System Identification, A Least Squares Approach. Cambridge University Press, 2007.
4. R. Adcock, "Note on the methods of least squares," The Analyst, vol. 4, no. 6, pp. 183-184, 1877.
5. -, "A problem in least squares," The Analyst, vol. 5, no. 2, pp. 53-54, 1878.
6. T. Söderström, "Errors-in-variables methods in system identification," Automatica, vol. 43, no. 6, pp. 939-958, 2007.
7. M. Milanese and A. Vicino, "Optimal estimation theory for dynamic sistems with set membership uncertainty: an overview," Automatica, vol. 27(6), pp. 997-1009, 1991.
8. E. Walter and H. Piet-Lahanier, "Estimation of parameter bounds from bounded-error data: a survey," Mathematics and Computers in simulation, vol. 32, pp. 449-468, 1990.
9. M. Milanese, J. Norton, H. Piet-Lahanier, and E. Walter, Eds., Bounding approaches to system identification. New York: Plenum Press, 1996.
10. J. Norton (Ed.), "Special issue on bounded-error estimation," Int. J. of Adapt. Control & Sign. Proces., vol. 8, no. 1, 1994.
11. -, "Special issue on bounded-error estimation," Int. J. of Adapt. Control & Sign. Proces., vol. 9, no. 1, 1995.
12. J. Norton, "Identification of parameter-bounds for armax models from records with bounded noise," International Journal of Control, vol. 45, pp. 375-390, 1987.
13. S. Veres and J. Norton, "Parameter-bounding algorithms for linear errors in variables models," in Proc. of IFAC/IFORS Symposium on Identification and System Parameter Estimation, 1991, pp. 1038-1043.
14. V. Cerone, "Feasible parameter set for linear models with bounded errors in all variable," Automatica, vol. 29, no. 6, pp. 1551-1555, 1993.
15. -, "Parameter bounds for armax models from records with bounded errors in variables," Int. J. Control, vol. 57, no. 1, pp. 225-235, 1993.
16. V. Cerone, D. Piga, and D. Regruto, "Parameters bounds evaluation for set-membership eiv problems through lmi relaxation techniques," DAUIN Internal Report 2009/09/14, 2009.
17. M. Laurent, "Sums of squares, moment matrices and optimization over polynomials," Emerging Applications of Algebraic Geometry, Vol. 149 of IMA Volumes in Mathematics and its Applications, M. Putinar and S. Sullivant (eds.), pp. 157-270, 2009.
18. P. Parrillo, "Semidefinite programming relaxations for semialgebraic problems," Mathematical Programming, vol. 96, pp. 293-320, 2003.
19. J. B. Lasserre, "Global optimization with polynomials and the problem of moments," SIAM Journal on Optimization, vol. 11, pp. 796-817, 2001.
20. D. Henrion and J. B. Lasserre, "Solving nonconvex optimization problems," IEEE Control Systems Magazine, vol. 24, no. 3, pp. 72-83, 2004.
21. H. Waki, S. Kim, M. Kojima, and M. Muramatsu, "Sums of squares and semidefinite programming relaxations for polynomial optimization problems with structured sparsity," SIAM Journal on Optimization, vol. 17, no. 1, pp. 218-242, 2006.
22. M. Kojima, S. Kim, and H. Waki, "Sparsity in sums of squares of polynomials," Mathematical Programming, vol. 103, pp. 45-62, 2005.
23. P. Parrillo, "Exploiting algebraic structure in sum of squares programs," Positive Polynomials in Control, D. Henrion and A. Garulli (eds.), pp. 181-194, 2005.
24. J. Lasserre, "Convergent semidefinite relaxations in polynomial optimization with sparsity," SIAM Journal on Optimization, vol. 17, no. 1, pp. 822-843, 2006. (Pubitemid 47265174)
25. J. F. Sturm, "Using SeDuMi 1.02, a MATLAB Toolbox for optimization over symmetric cones," Optim. Methods Software, vol. 11, no. 12, pp. 625-653, 1999.