Robust set-membership filtering for systems with missing measurement: a linear matrix inequality approach
Robust set-membership filtering for systems with missing measurement: a linear matrix inequality approach
- Author(s): F. Yang and Y. Li
- DOI: 10.1049/iet-spr.2009.0244
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- Author(s): F. Yang 1 and Y. Li 2
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View affiliations
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Affiliations:
1: School of Information Science and Engineering, East China University of Science and Technology, Shanghai, People's Republic of China
2: Department of Information Systems and Computing, Brunel University, Uxbridge, UK
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Affiliations:
1: School of Information Science and Engineering, East China University of Science and Technology, Shanghai, People's Republic of China
- Source:
Volume 6, Issue 4,
June 2012,
p.
341 – 347
DOI: 10.1049/iet-spr.2009.0244 , Print ISSN 1751-9675, Online ISSN 1751-9683
This study addresses the robust set-membership finite-horizon filtering problem for a class of discrete time-varying systems with missing measurement and polytopic uncertainties in the presence of unknown-but-bounded process and measurement noises. A robust set-membership filter is developed and a recursive algorithm is derived for computing the state estimate ellipsoid that is guaranteed to contain the true state. An optimal possible estimate set is computed recursively by solving the semi-definite programming problem. Simulation results are provided to demonstrate the effectiveness of the proposed method.
Inspec keywords: uncertain systems; filtering theory; linear matrix inequalities; discrete time systems; recursive estimation; state estimation; mathematical programming; time-varying systems
Other keywords:
Subjects: Other topics in statistics; Optimisation techniques; Other topics in statistics; Algebra; Optimisation techniques; Filtering methods in signal processing; Signal processing theory; Algebra
References
-
-
1)
- Z. Wang , F. Yang , D.W.C. Ho , X. Liu . Robust H∞ filtering for stochastic time-delay systems with missing measurements. IEEE Trans. Signal Process. , 7 , 2579 - 2587
-
2)
- M.C. de Oliveira , J. Bernussou , J.C. Geromel . A new discrete-time robust stability condition. Syst. Control Lett. , 261 - 265
-
3)
- S.P. Bhattacharyya , H. Chapellat , L.H. Keel . (1995) Robust control: the parametric approach.
-
4)
- L. El Ghaoui , G. Calafiore . Robust filtering for discrete-time systems with bounded noise and parametric uncertainty. IEEE Trans. Autom. Control , 7 , 1084 - 1089
-
5)
- F.C. Schweppe . Recursive state estimation: unknown but bounded errors and system inputs. IEEE Trans. Autom. Control , 1 , 22 - 28
-
6)
- F. Yang , Y. Li . Set-membership fuzzy filtering for nonlinear discrete-time systems. IEEE Trans. Syst. Man Cybern. B , 1 , 116 - 124
-
7)
- L. Xie , L. Lu , D. Zhang , H. Zhang . Improved robust ℋ2 and ℋ∞ filtering for uncertain discrete-time systems. Automatica , 873 - 880
-
8)
- A.V. Savkin , I.R. Petersen , S.O.R. Moheimani . Model validation and state estimation for uncertain continuous-time systems with missing discrete-continuous data. Comput. Electr. Eng. , 1 , 29 - 43
-
9)
- D.G. Maskarov , J.P. Norton . State bounding with ellipsoidal set description of the uncertainty. Int. J. Control , 5 , 847 - 866
-
10)
- P.L. Combettes . The foundations of set theoretic estimation. Proc. IEEE , 2 , 182 - 208
-
11)
- R.E. Kalman . A new approach to linear filtering and prediction problems. Trans. ASME-J. Basic Eng. , 35 - 45
-
12)
- J. Shamma , K. Tu . Set-valued observers and optimal disturbance rejection. IEEE Trans. Autom. Control , 2 , 253 - 264
-
13)
- G. Zames . Feedback and optimal sensitivity: model reference transformation, multiplicative semi-norms and approximate inverses. IEEE Trans. Autom. Control , 2 , 301 - 320
-
14)
- F. Yang , Y.S. Hung . Robust mixed H2/H∞ filtering with regional pole assignment for uncertain discrete-time systems. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. , 8 , 1236 - 1241
-
15)
- H.S. Witsenhausen . Sets of possible states of linear systems given perturbed observations. IEEE Trans. Autom. Control , 5 , 556 - 558
-
16)
- Polyak, B., Nazin, S., Durieu, C., Walter, E.: `Ellipsoidal estimation under model uncertainty', 15thTriennial World Congress, 2002, Barcelona, Spain.
-
17)
- Y. Nesterov , A. Nemirovski . (1994) Interior point polynomial methods in convex programming: theory and applications.
-
18)
- A.V. Savkin , I.R. Petersen . Robust state estimation and model validation for discrete-time uncertain systems with a deterministic description of noise and uncertainty. Automatica , 2 , 271 - 274
-
19)
- Löfberg, J.: `YALMIP: a toolbox for modeling and optimization in matlab', Proc. IEEE CACSD Symp., 2004, Taipei, Taiwan.
-
20)
- Z. Wang , F. Yang , D.W.C. Ho , X. Liu . Robust finite-horizon filtering for stochastic systems with missing measurements. IEEE Signal Process. Lett. , 6 , 437 - 440
-
21)
- N.E. Nahi . Optimal recursive estimation with uncertain observation. IEEE Trans. Inf. Theory , 457 - 462
-
22)
- D.R. Morrell , W.C. Stirling . Set-valued filtering and smoothing. IEEE Trans. Syst. Man Cybern. , 1 , 184 - 193
-
23)
- C. Durieu , E. Walter , B. Polyak . Multi-input multi-output ellipsoidal state bounding. J. Optim. Theory Appl. , 273 - 303
-
24)
- B.D.O. Anderson , J.R. Moore . (1979) Optimal filtering.
-
25)
- F. Yang , Y. Li . Set-membership filtering for discrete-time systems with nonlinear equality constraints. IEEE Trans. Autom. Control , 10 , 2480 - 2486
-
26)
- W.S. Ra , S.H. Jin , J.B. Park . Set-valued estimation approach to recursive robust ℋ∞ filtering. IEE Proc., Control Theory Appl. , 6 , 773 - 782
-
27)
- Y.S. Hung , F. Yang . Robust H∞ filtering for discrete time-varying uncertain systems with a known deterministic input. Int. J. Control , 15 , 1159 - 1169
-
28)
- D.P. Bertsekas , I.B. Rhodes . Recursive state estimation for a set-membership description of uncertainty. IEEE Trans. Autom. Control , 2 , 117 - 128
-
29)
- S. Boyd , L.E. Ghaoui , E. Feron , V. Balakrishnan . (1994) Linear matrix inequalities in system and control theory.
-
30)
- D. Peaucelle , D. Arzelier , O. Bachelier , J. Bernussou . A new robust -stability condition for real convex polytopic uncertainty. Syst. Control Lett. , 1 , 21 - 30
-
31)
- J.F. Sturm . Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. , 625 - 653
-
32)
- A.V. Savkin , I.R. Petersen . Robust filtering with missing data and a deterministic description of noise and uncertainty. Int. J. Syst. Sci. , 4 , 373 - 390
-
33)
- F. Yang , Y. Li . Set-membership filtering for systems with sensor saturation. Automatica , 8 , 1896 - 1902
-
34)
- A.V. Savkin , I.R. Petersen . Recursive state estimation for uncertain systems with an integral quadratic constraint. IEEE Trans. Autom. Control , 6 , 1080 - 1083
-
35)
- F. Yang , Z. Wang , Y.S. Hung . Robust kalman filtering for discrete time-varying uncertain systems with multiplicative noises. IEEE Trans. Autom. Control , 7 , 1179 - 1183
-
36)
- A.B. Kurzhanski , I. Valyi . (1996) Ellipsoidal calculus for estimation and control.
-
37)
- L. Vandenberghe , S. Boyd . Semidefinite programming. SIAM Review. , 1 , 49 - 95
-
38)
- R.E. Skelton , T. Iwasaki , K.M. Grigoriadis . (1998) A unified algebraic approach to linear control design.
-
1)
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