A sparsification approach to set membership identification of switched affine systems

IEEE Transactions on Automatic Control

Volumn 57, Issue 3, 2012, Pages 634-648

  Ozay, Necmiye ^a   Sznaier, Mario ^b   Lagoa, Constantino M ^c   Camps, Octavia I ^b  

^a California Institute of Technology   (United States)

^b Northeastern University   (United States)

^c The Pennsylvania State University   (United States)

Author keywords

Hybrid systems; piecewise affine systems; set membership identification; sparse signal recovery

Indexed keywords

AFFINE HYBRID SYSTEMS; AFFINE MODEL; BOUNDED NOISE; COMPUTER VISION APPLICATIONS; CONVEX RELAXATION; CONVEX SET; DISCRETE-TIME; DYNAMIC TEXTURES; INPUT/OUTPUT DATUM; NON-TRIVIAL; NP-HARD; NUMBER OF SWITCHES; PIECEWISE AFFINE SYSTEMS; PRIORI INFORMATION; ROBUST IDENTIFICATION; SET MEMBERSHIP; SET-MEMBERSHIP IDENTIFICATION; SPARSE SIGNALS; SPARSIFICATION; SWITCHED AFFINE SYSTEMS; SWITCHING SEQUENCE;

COMPUTER APPLICATIONS; CONVEX OPTIMIZATION; HYBRID SYSTEMS; SET THEORY; SIGNAL RECONSTRUCTION;

RELAXATION PROCESSES;

EID: 84857770002     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2011.2166295     Document Type: Article

References (40)

1. S. Paoletti, A. Juloski, G. Ferrari-Trecate, and R. Vidal, "Identification of hybrid systems: A tutorial," Eur. J. Control, vol. 13, no. 2, pp. 242-260, May 2007.
2. Y. Ma and R. Vidal, "A closed form solution to the identification of hybrid ARX models via the identification of algebraic varieties," Hybrid Syst. Comput. Control, pp. 449-465, Mar. 2005. (Pubitemid 41252084)
3. A. Bemporad, A. Garulli, S. Paoletti, and A. Vicino, "A bounded-error approach to piecewise affine system identification," IEEE Trans. Autom. Control, vol. 50, no. 10, pp. 1567-1580, Oct. 2005. (Pubitemid 41555605)
4. J. Roll, A. Bemporad, and L. Ljung, "Identification of piecewise affine systems via mixed-integer programming," Automatica, vol. 40, pp. 37-50, 2004.
5. A. Juloski, S. Wieland, and W. P. M. H. Heemels, "A bayesian approach to identification of hybrid systems," IEEE Trans. Autom. Control, vol. 50, no. 10, pp. 1520-1533, Oct. 2005. (Pubitemid 41555602)
6. G. Ferrari-Trecate, M. Muselli, D. Liberati, and M. Morari, "A clustering technique for the identification of piecewise affine systems," Automatica, vol. 39, pp. 205-217, Feb. 2003.
7. H. Nakada, K. Takaba, and T. Katayama, "Identification of piecewise affine systems based on statistical clustering technique," Automatica, vol. 41, no. 5, pp. 905-913, May 2005. (Pubitemid 40352405)
8. D. Donoho, M. Elad, and V. Temlyakov, "Stable recovery of sparse overcomplete representations in the presence of noise," IEEE Transactions on Inf. Theory, vol. 52, no. 1, pp. 6-18, Jan. 2006. (Pubitemid 43263116)
9. J. Tropp, "Just relax: Convex programming methods for identifying sparse signals in noise," IEEE Trans. Inf. Theory, vol. 52, no. 3, pp. 1030-1051, Mar. 2006. (Pubitemid 46444890)
10. R. Vidal, A. Chiuso, and S. Soatto, "Observability and identifiability of jump linear systems," in Proc, 41st IEEE Conf. Decision and Control, , Dec. 2002, vol. 4, pp. 3614-3619.
11. J. Lygeros, K. H. Johansson, S. N. Simic, J. Zhang, and S. S. Sastry, "Dynamical properties of hybrid automata," IEEE Trans. Autom. Control, vol. 48, no. 1, pp. 2-17, Jan. 2003.
12. A. Gionis and H. Mannila, "Segmentation algorithms for time series and sequence data," in SIAM Int. Conf. Data Mining, 2005, Tutorial.
13. 2-Minimization: Simple Derivations and Extensions," Tech. Rep. Rice University, 2008.
14. Y. C. Eldar and M. Mishali, "Robust recovery of signals from a structured union of subspaces," IEEE Trans. Inf. Theory, vol. 55, no. 11, pp. 5302-5316, Nov. 2009.
15. M. Stojnic, F. Parvaresh, and B. Hassibi, "On the reconstruction of block-sparse signals with an optimal number of measurements," IEEE Trans. Signal Processing, vol. 57, no. 8, pp. 3075-3085, Aug. 2009.
16. N. Ozay, "Convex Relaxations for Robust Identification of Hybrid Models," Ph.D., Northeastern University, , 2010.
17. M. Fazel, H. Hindi, and S. Boyd, "Log-det heuristic for matrix rank minimization with applications to hankel and euclidean distance matrices," in Proc. American Control Conf., Jun. 2003.
18. M. Lobo, M. Fazel, and S. Boyd, "Portfolio optimization with linear and fixed transaction costs," Annals of Operations Research, vol. 152, no. 1, pp. 376-394, Jul. 2007.
19. E. J. Candes, M. Wakin, and S. Boyd, "Enhancing sparsity by reweighted l1 minimization," Journal of Fourier Analysis and Applications, vol. 14, no. 5, pp. 877-905, Dec. 2008.
20. J. Woods, Multidimensional Signal, Image and Video Processing and Coding. : Academic Press, 2006.
21. R. Vidal, "Identification of spatial-temporal switched ARX systems," in Proc. 46th IEEE Conf. Decision and Control, Dec. 2007, pp. 4675-4680. (Pubitemid 351277881)
22. E. Amaldi and M. Mattavelli, "The MIN PFS problem and piecewise linear model estimation," Discrete Appl. Math., vol. 118, no. 1-2, pp. 115-143, Apr. 2002.
23. R. Vidal, S. Soatto, Y. Ma, and S. Sastry, "An algebraic geometric approach to the identification of a class of linear hybrid systems," in Proc. 42nd IEEE Conf. Decision and Control, Dec. 2003, pp. 167-172.
24. R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, 2nd ed. Hoboken: Wiley, 2000.
25. R. Vidal, Y. Ma, and S. Sastry, "Generalized principal component analysis (gpca)," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 12, pp. 1945-1959, Dec. 2005. (Pubitemid 43051391)
26. W. Hong, J. Wright, K. Huang, and Y. Ma, "Multiscale hybrid linear models for lossy image representation," IEEE Trans. Image Processing, vol. 15, no. 12, pp. 3655-3671, Dec. 2006. (Pubitemid 44811680)
27. A. B. Chan and N. Vasconcelos, "Mixtures of dynamic textures," in Proc. IEEE Int. Conf. Computer Vision, 2005, vol. 1, pp. 641-647. (Pubitemid 44055016)
28. L. Cooper, J. Liu, and K. Huang, "Spatial segmentation of temporal texture using mixture linear models," in Workshop on Dynamical Vision, 2005, pp. 142-150.
29. U. Gargi, R. Kasturi, and S. H. Strayer, "Performance characterization of video-shot-change detection methods," IEEE Trans. Circuits Syst. for Video Technol., vol. 10, no. 1, pp. 1-13, Feb. 2000. (Pubitemid 30559996)
30. Y. Boon-Lock and B. Liu, "A unified approach to temporal segmentation of motion jpeg and mpeg compressed video," in Proc. Int. Conf. Multimedia Comput. and Syst., May 1995, pp. 81-88.
31. W. Rand, "Objective criteria for the evaluation of clustering methods," J. Amer. Statistical Assoc., vol. 66, pp. 846-850, 1971.
32. E. J. Candès, J. K. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure and Appl. Math., vol. 59, no. 8, pp. 1207-1223, Aug. 2006. (Pubitemid 43988295)
33. B. K. Natarajan, "Sparse approximate solutions to linear systems," SIAM J. Computing, vol. 24, no. 2, pp. 227-234, 1995.
34. E. Amaldi and V. Kann, "On the approximability of minimizing nonzero variables or unsatisfied relations in linear systems," Theoretical Comp. Sci., vol. 209, no. 1-2, pp. 237-260, 1998. (Pubitemid 128450440)
35. J. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. Inf. Theory, vol. 50, no. 10, pp. 2231-2242, Oct. 2004.
36. J. A. Tropp and A. C. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Trans. Inf. Theory, vol. 53, pp. 4655-4666, 2007.
37. D. Needell and R. Vershynin, "Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit," Foundations of Comput. Math., vol. 9, no. 3, pp. 317-334, 2009.
38. A. M. Bruckstein, D. L. Donoho, and M. Elad, "From sparse solutions of systems of equations to sparse modeling of signals and images," SIAM Rev., vol. 51, no. 1, pp. 34-81, 2009.
39. J.-B. Hiriart-Urruty and C. Lemarechal, Convex Analysis and Minimization Algortihms II: Advanced Theory and Bundle Methods. Berlin, Germany: Springer-Verlag, 1993, vol. 306, Grundlehrer der mathematischen Wissenschaften.
40. M. Fazel, H. Hindi, and S. Boyd, "A rank minimization heuristic with application to minimum order system approximation," in Proc. American Control Conf., Jun. 2001.