This paper deals with the problem of joint state and parameter estimation based on a set adaptive observer design. The problem is formulated and solved for an LPV (linear parameter-varying) system. The resolution methodology avoids the exponential complexity obstruction usually encountered in the set-membership parameter estimation. A simulation example is presented to illustrate the efficiency of the proposed approach.
Issue Section:
Research Papers
References
1.
Besançon
, G.
, ed., 2007
, Nonlinear Observers and Applications
(Lecture Notes in Control and Inforamtion Science), Vol. 363
, Springer Verlag
, Berlin
.2.
Nijmeijer
, H.
, and Fossen
, T. I.
, 1999
, New Directions in Nonlinear Observer Design
, Springer-Verlag
, London
.3.
Bokor
, J.
, and Balas
, G.
, 2004
, “Detection Filter Design for LPV Systems—A Geometric Approach
,” Automatica
, 40
, pp. 511
–518
.10.1016/j.automatica.2003.11.0034.
Javad
, M.
, and Carsten
, S. W.
, eds., 2012
, Control of Linear Parameter Varying Systems With Applications
, Springer
, New York.
5.
Lee
, L. H.
, 1997
, “Identification and Robust Control of Linear Parameter-Varying Systems
,” Ph.D. thesis, University of California at Berkeley
, Berkeley, California
.6.
dos Santos
, P. L.
, Perdicoúlis
, T. P. A.
, Novara
, C.
, Ramos
, J. A.
, and Rivera
, D. E.
, eds., 2011
, Linear Parameter-Varying System Identification: New Developments and Trends
(Advanced Series in Electrical and Computer Engineering), Vol. 14
, World Scientific
, Singapore
.7.
Marcos
, A.
, and Balas
, J.
, 2004
, “Development of Linear-Parameter-Varying Models for Aircraft
,” J. Guid. Control Dyn.
, 27
(2
), pp. 218
–228
.10.2514/1.91658.
Shamma
, J.
, and Cloutier
, J.
, 1993
, “Gain-Scheduled Missile Autopilot Design Using Linear Parameter-Varying Transformations
,” J. Guid. Control Dyn.
, 16
(2
), pp. 256
–261
.10.2514/3.209979.
Tan
, W.
, 1997
, “Applications of Linear Parameter-Varying Control Theory
,” Ph.D. thesis, Department of Mechanical Engineering, University of California at Berkeley
, Berkeley, CA.10.
Jaulin
, L.
, 2002
, “Nonlinear Bounded-Error State Estimation of Continuous Time Systems
,” Automatica
, 38
(2
), pp. 1079
–1082
.10.1016/S0005-1098(01)00284-911.
Raïssi
, T.
, Ramdani
, N.
, and Candau
, Y.
, 2004
, “Set Membership State and Parameter Estimation for Systems Described by Nonlilear Differential Equations
,” Automatica
, 40
, pp. 1771
–1777
.10.1016/j.automatica.2004.05.00612.
Kieffer
, M.
, and Walter
, E.
, 2004
, “Guaranteed Nonlinear State Estimator for Cooperative Systems
,” Numer. Algorithms
, 37
, pp. 187
–198
.10.1023/B:NUMA.0000049466.96588.a613.
Müller
, M.
, 1920
, “Überdas Fundamental Theorem in der Theorie der Gewöhnlichen Differentialgleichungen
,” Math. Z
, 26
, pp. 619
–645
.10.1007/BF0147547714.
Bernard
, O.
, and Gouzé
, J. L.
, 2004
, “Closed Loop Observers Bundle for Uncertain Biotechnological Models
,” J. Process Control
, 14
, pp. 765
–774
.10.1016/j.jprocont.2003.12.00615.
Gouzé
, J. L.
, Rapaport
, A.
, and Hadj-Sadok
, M. Z.
, 2000
, “Interval Observers for Uncertain Biological Systems
,” Ecol. Model.
, 133
, pp. 46
–56
.16.
Mazenc
, F.
, and Bernard
, O.
, 2011
, “Interval Observers for Linear Time-Invariant Systems With Disturbances
,” Automatica
, 47
(1
), pp. 140
–147
.10.1016/j.automatica.2010.10.01917.
Raïssi
, T.
, Videau
, G.
, and Zolghadri
, A.
, 2010
, “Interval Observers Design for Consistency Checks of Nonlinear Continuous-Time Systems
,” Automatica
, 46
(3
), pp. 518
–527
.10.1016/j.automatica.2009.12.00518.
Jaulin
, L.
, and Walter
, E.
, 1993
, “Set Inversion via Interval Analysis for Nonlinear Bounded-Error Estimation
,” Automatica
, 29
(4
), pp. 1053
–1064
.10.1016/0005-1098(93)90106-419.
Johnson
, T.
, and Tucker
, W.
, 2008
, “Rigorous Parameter Reconstruction for Differential Equations With Noisy Data
,” Automatica
, 44
(9
), pp. 2422
–2426
.10.1016/j.automatica.2008.01.03220.
Efimov
, D.
, 2006
, “Dynamical Adaptive Synchronization
,” Int. J. Adapt. Control Signal Process.
, 20
(9
), pp. 491
–507
.10.1002/acs.91421.
Farza
, M.
, M'Saad
, M.
, Maatoug
, T.
, and Kamoun
, M.
, 2009
, “Adaptive Observers for Nonlinearly Parameterized Class of Nonlinear Systems
,” Automatica
, 45
(10
), pp. 2292
–2299
.10.1016/j.automatica.2009.06.00822.
Stamnes
, Ø. N.
, Aamo
, O. M.
, and Kaasa
, G.-O.
, 2011
, “Redesign of Adaptive Observers for Improved Parameter Identification in Nonlinear Systems
,” Automatica
, 47
(2
), pp. 403
–410
.10.1016/j.automatica.2010.11.00523.
Xu
, A.
, and Zhang
, Q.
, 2004
, “Residual Generation for Fault Diagnosis in Linear Time-Varying Systems
,” IEEE Trans. Autom. Control
, 49
(5
), pp. 767
–772
.10.1109/TAC.2004.82598324.
Zemouche
, A.
, and Boutayeb
, M.
, 2009
, “A Unified Adaptive Observer Synthesis Method for a Class of Systems With Both Lipschitz and Monotone Nonlinearities
,” Syst. Control Lett.
, 58
(4
), pp. 282
–288
.10.1016/j.sysconle.2008.11.00725.
Zhang
, Q.
, 2002
, “Adaptive Observer for Multiple-Input-Multiple-Output Linear Time Varying Systems
,” IEEE Trans. Autom. Control
, 47
(3
), pp. 525
–529
.10.1109/9.98915426.
Smith
, H. L.
, 1995
, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems
, Vol. 41
, Surveys and Monographs, AMS
, Providence
, RI.27.
Anderson
, B. D. O.
, 1977
, “Exponential Stability of Linear Equations Arising in Adaptive Identification
,” IEEE Trans. Autom. Control
, 22
, pp. 83
–88
.10.1109/TAC.1977.110140628.
Yuan
, J. S.-C.
, and Wonham
, W. M.
, 1977
, “Probing Signals for Model Reference Identification
,” IEEE Trans. Autom. Control
, 22
, pp. 530
–538
.10.1109/TAC.1977.110155629.
Sanders
, J.
, Verhulst
, F.
, and Murdock
, J.
, 2007
, Averaging Methods in Nonlinear Dynamical Systems
, Springer
, New York
.30.
Raïssi
, T.
, Efimov
, D.
, and Zolghadri
, A.
, 2012
, “Interval State Estimation for a Class of Nonlinear Systems
,” IEEE Trans. Autom. Control
, 57
(1
), pp. 260
–265
.10.1109/TAC.2011.216482031.
Bogoliubov
, N. N.
, and Mitropolskii
, Yu, A.
, 1961
, Asymptotic Methods in the Theory of Nonlinear Oscillations
, Gordon and Breach
, New York
.32.
Blanke
, M.
, Kinnaert
, M.
, Lunze
, J.
, and Staroswiecki
, M.
, 2006
, Diagnosis and Fault Tolerant Control
, Springer-Verlag
, Berlin
, 2nd ed.33.
Chen
, J.
, and Patton
, R. J.
, 1999
, Robust Model-Based Fault Diagnosis for Dynamic Systems
, Kluwer Academic Publishers
, London.34.
Ferrari
, R.
, Parisini
, T.
, and Polycarpou
, M. M.
, 2009
, “Distributed Fault Diagnosis With Overlapping Decompositions: An Adaptive Approximation Approach
,” IEEE Trans. Autom. Control
, 54
(4
), pp. 794
–799
.10.1109/TAC.2008.200959135.
Puig
, V.
, 2010
, “Fault Diagnosis and Fault Tolerant Control Using Set–Membership Approaches: Application to Real Case Studies
,” Int. J. Appl. Math. Comput. Sci.
, 20
(4
), pp. 619
–635
.10.2478/v10006-010-0046-y36.
Rosa
, P.
, Silvestre
, C.
, Shamma
, J. S.
, and Athans
, M.
, 2010
, “Fault Detection and Isolation of LTV Systems Using Set-Valued Observers
,” Proceedings of 49th IEEE Conference on Decision and Control
, Atlanta, pp. 768
–773
.37.
Ding
, S. X.
, 2008
, Model-Based Fault Diagnosis Techniques. Design Schemes, Algorithms, and Tools
, Springer, Heidelberg
, Berlin
.38.
Blesa
, J.
, Puig
, V.
, and Bolea
, Y.
, 2010
, “Fault Detection Using Interval LPV Models in an Open-Flow Canal
,” Control Eng. Pract.
, 18
(5
), pp. 460
–470
.10.1016/j.conengprac.2010.01.00239.
Join
, C.
, Sira-Ramirez
, H.
, and Fliess
, M.
, 2005
, “Control of an Uncertain Three Tank System via On-Line Parameter Identification and Fault Detection
,” Proceedings of 16th IFAC World Congress
, Prague
.40.
Theilliol
, D.
, Noura
, H.
, and Ponsart
, J.-C.
, 2002
, “Fault Diagnosis and Accommodation of a Three-Tank System Based on Analytical Redundancy
,” ISA Trans.
, 41
, pp. 365
–
382
.10.1016/S0019-0578(07)60094-941.
Zolghadri
, A.
, Henry
, D.
, and Monsion
, M.
, 1996
, “Design of Nonlinear Observers for Fault Diagnosis: A Case Study
,” Control Eng. Pract.
, 4
(11
), pp. 1535
–1544
.10.1016/0967-0661(96)00167-0Copyright © 2014 by ASME
You do not currently have access to this content.
