Multi-input multi-output ellipsoidal state bounding

Journal of Optimization Theory and Applications

Volumn 111, Issue 2, 2001, Pages 273-303

  Durieu, C ^a   Walter, E ^b   Polyak, B ^c  

^a Centre National de la Recherche Scientifique   (France)

^b CNRS   (France)

^c TRAPEZNIKOV INSTITUTE OF CONTROL SCIENCES   (Russian Federation)

Author keywords

Bounded noise; Ellipsoidal bounding; Identification; Set membership estimation; State estimation

Indexed keywords

STATE ESTIMATION;

BOUNDED NOISE; ELLIPSOIDAL BOUNDING; IDENTIFICATION; KALMAN-FILTERING; MULTI-INPUT MULTI-OUTPUT; OUTPUT STATE; PHASE BASED; SET-MEMBERSHIP ESTIMATION; UNCERTAINTY;

MIMO SYSTEMS;

EID: 0039594871     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1011978200643     Document Type: Article

References (34)

1. WITSENHAUSEN, H. S., Sets of Possible States of Linear Systems Given Perturbed Observations, IEEE Transactions on Automatic Control, Vol. 13, pp. 556-558, 1968.
2. SCHWEPPE, F. C., Recursive State Estimation: Unknown but Bounded Errors and System Inputs, IEEE Transactions on Automatic Control, Vol. 13, pp. 22-28, 1968.
3. BERTSEKAS, D. P., and RHODES, I. B., Recursive State Estimation for a Set-Membership Description of Uncertainty, IEEE Transactions on Automatic Control, Vol. 16, pp. 117-128, 1971.
4. KURZHANSKI, A. B., Control and Observation under Uncertainty, Nauka, Moscow, 1977 (in Russian).
5. CHERNOUSKO, F. L., State Estimation for Dynamic Systems, CRC Press, Boca Raton, Florida, 1994.
6. KURZHANSKI, A. B., and VALYI, I., Ellipsoidal Calculus for Estimation and Control, Birkhäuser, Boston, Massachusetts, 1996.
7. POLYAK, B. T., Convexity of Quadratic Transformations and Its Use in Control and Optimization, Journal of Optimization Theory and Applications, Vol. 99, pp. 553-583, 1998.
8. CHERNOUSKO, F. L., and ROKITYANSKII, D. YA., Ellipsoidal Bounds on Reachable Sets of Dynamical Systems with Matrices Subjected to Uncertain Perturbations, Journal of Optimization Theory and Applications, Vol. 104, pp. 1-19, 2000.
9. COMBETTES, P. L., The Foundations of Set-Theoretic Estimation, Proceedings of the IEEE, Vol. 81, pp. 182-208, 1993.
10. DELLER, J. R., NAYERI, M., and ODEH, S. F., Least-Square Identification with Error Bounds for Real-Time Signal Processing and Control, Proceedings of the IEEE, Vol. 81, pp. 813-849, 1993.
11. WALTER, E., Editor, Special Issue on Parameter Identifications with Error Bound, Mathematics and Computers in Simulation, Vol. 32, pp. 447-607, 1990.
12. NORTON, J. P., Editor, Special Issue on Bounded-Error Estimation, Part 1, International Journal of Adaptative Control and Signal Processing, Vol. 8, pp. 1-118, 1994.
13. NORTON, J. P., Editor, Special Issue on Bounded-Error Estimation, Part 2, International Journal of Adaptative Control and Signal Processing, Vol. 9, pp. 1-132, 1995.
14. MILANESE, M., NORTON, J., PIET-LAHANIER, H., and WALTER, E., Editors, Bounding Approaches to System Identification, Plenum Press, New York, NY, 1996.
15. WALTER, E., and PIET-LAHANIER, H., Exact Recursive Polyhedral Description of the Feasible Parameter Set for Bounded-Error Models, IEEE Transactions on Automatic Control, Vol. 34, pp. 911-915, 1989.
16. BELFORTE, G., BONA, B., and CERONE, V., Parameter Estimation Algorithms for a Set-Membership Description of Uncertainty, Automatica, Vol. 26, pp. 887-898, 1990.
17. FOGEL, E., and HUANG, Y. F., On the Value of Information in System Identification: Bounded Noise Case, Automatica, Vol. 18, pp. 229-238, 1982.
18. MAKSAROV, D. G., and NORTON, J. P., State Bounding with Ellipsoidal Set Description of the Uncertainty, International Journal of Control, Vol. 65, pp. 847-866, 1996.
19. GOLLAMUDI, S., NAGARAJ, S., KAPOOR, S., and HUANG, Y. F., Set-Membership State Estimation with Optimal Bounding Ellipsoids, Proceedings of the International Symposium on Information Theory and Its Applications, pp. 262-265, 1996.
20. DURIEU, C., POLYAK, B., and WALTER, E., Trace Versus Determinant in Ellipsoidal Outer Bounding with Application to State Estimation, 13th IFAC World Congress, Vol. I, pp. 43-48, 1996.
21. DURIEU, C., POLYAK, B., and WALTER, E., Ellipsoidal State Outer Bounding for MIMO Systems via Analytical Techniques, 1996 CESA IMACS IEEE-SMC Multiconference, Symposium on Modelling, Analysis, and Simulation, Vol. 2, pp. 843-848, 1996.
22. DURIEU, C., WALTER, E., and POLYAK, B., Ellipsoidal Bounding Techniques for Parameter Tracking, 11th IFAC Symposium on System Identification, SYSID'97, Vol. 4, pp. 1777-1782, 1997.
23. SCHWEPPE, F. C., Uncertain Dynamic Systems, Prentice Hall, Englewood Cliffs, New Jersey, 1973.
24. KAHAN, W., Circumscribing an Ellipsoid about the Intersection of Two Ellipsoids, Canadian Mathematical Bulletin, Vol. 2, pp. 437-441, 1968.
25. BOYD, S., EL GHAOUI, L., FERON, E., and BALAKRISHNAN, V., Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, Philadelphia, Pennsylvania, Vol. 15, 1994.
26. NESTEROV, Y., and NEMIROVSKII, A., Interior-Point Polynomial Algorithms in Convex Programming, SIAM Studies in Applied Mathematics, Philadelphia, Pennsylvania, Vol. 13, 1994.
27. HORN, R. A., and JOHNSON, C. R., Matrix Analysis, Cambridge University Press, Cambridge, England, 1985.
28. BERGER, M., Géométrie, CEDIC/Nathan, Paris, France, 1979.
29. KISELEV, O. N., and POLYAK, B. T., Ellipsoidal Estimation with Respect to a Generalized Criterion, Automation and Remote Control, Vol. 52, pp. 1281-1292, 1992 (English Translation).
30. KREINDLER, E., and JAMESON, A., Conditions for Nonnegativeness of Partioned Matrices, IEEE Transactions on Automatic Control, Vol. 17, pp. 147-148, 1972.
31. RESHETNYAK, Y., Summation of Ellipsoids in a Guaranteed Estimation Problem, Journal of Applied Mathematics and Mechanics (PMM), Vol. 53, pp. 249-254, 1989.
32. BERTSEKAS, D. P., Nonlinear Programming, Athena Publishers, Belmont, Massachusetts, 1998.
33. PRONZATO, L., WALTER, E., and PIET-LAHANIER, H., Mathematical Equivalence of Two Ellipsoidal Algorithms for Bounded-Error Estimation, 28th IEEE Conference on Decision and Control, pp. 1952-1955, 1989.
34. DURIEU, C., WALTER, E., and POLYAK, B., Set-Membership Estimation with the Trace Criterion Made Simpler Than with the Determinant Criterion, 12th IFAC Symposium on System Identification, SYSID'2000, CD-ROM, 2000.