Research Papers

Set Adaptive Observers for Linear Parameter-Varying Systems: Application to Fault Detection

[+] Author and Article Information
Denis Efimov

Non-A project at INRIA - LNE,
Parc Scientifique de la Haute Borne,
40 avenue Halley, Bât.A Park Plaza,
Villeneuve d'Ascq 59650, France
e-mail: Denis.Efimov@inria.fr

Tarek Raïssi

Conservatoire National des Arts et Métiers,
Département EASY, Cedric – laetitia,
292, Rue St-Martin, case 2D2P10,
75141 Paris Cedex 03, France
e-mail: Tarek.Raıssi@cnam.fr

Ali Zolghadri

University of Bordeaux,
IMS-lab, Automatic control group,
351 cours de la libération,
Talence 33405, France
e-mail: Ali.Zolghadri@ims-bordeaux.fr

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 7, 2012; final manuscript received July 11, 2013; published online December 2, 2013. Assoc. Editor: John B. Ferris.

J. Dyn. Sys., Meas., Control 136(2), 021006 (Dec 02, 2013) (7 pages) Paper No: DS-12-1132; doi: 10.1115/1.4025797 History: Received May 07, 2012; Revised July 11, 2013

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.

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Besançon, G., ed., 2007, Nonlinear Observers and Applications (Lecture Notes in Control and Inforamtion Science), Vol. 363, Springer Verlag, Berlin.
Nijmeijer, H., and Fossen, T. I., 1999, New Directions in Nonlinear Observer Design, Springer-Verlag, London.
Bokor, J., and Balas, G., 2004, “Detection Filter Design for LPV Systems—A Geometric Approach,” Automatica, 40, pp. 511–518. [CrossRef]
Javad, M., and Carsten, S. W., eds., 2012, Control of Linear Parameter Varying Systems With Applications, Springer, New York.
Lee, L. H., 1997, “Identification and Robust Control of Linear Parameter-Varying Systems,” Ph.D. thesis, University of California at Berkeley, Berkeley, California.
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.
Marcos, A., and Balas, J., 2004, “Development of Linear-Parameter-Varying Models for Aircraft,” J. Guid. Control Dyn., 27(2), pp. 218–228. [CrossRef]
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. [CrossRef]
Tan, W., 1997, “Applications of Linear Parameter-Varying Control Theory,” Ph.D. thesis, Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA.
Jaulin, L., 2002, “Nonlinear Bounded-Error State Estimation of Continuous Time Systems,” Automatica, 38(2), pp. 1079–1082. [CrossRef]
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. [CrossRef]
Kieffer, M., and Walter, E., 2004, “Guaranteed Nonlinear State Estimator for Cooperative Systems,” Numer. Algorithms, 37, pp. 187–198. [CrossRef]
Müller, M., 1920, “Überdas Fundamental Theorem in der Theorie der Gewöhnlichen Differentialgleichungen,” Math. Z, 26, pp. 619–645. [CrossRef]
Bernard, O., and Gouzé, J. L., 2004, “Closed Loop Observers Bundle for Uncertain Biotechnological Models,” J. Process Control, 14, pp. 765–774. [CrossRef]
Gouzé, J. L., Rapaport, A., and Hadj-Sadok, M. Z., 2000, “Interval Observers for Uncertain Biological Systems,” Ecol. Model., 133, pp. 46–56. [CrossRef]
Mazenc, F., and Bernard, O., 2011, “Interval Observers for Linear Time-Invariant Systems With Disturbances,” Automatica, 47(1), pp. 140–147. [CrossRef]
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. [CrossRef]
Jaulin, L., and Walter, E., 1993, “Set Inversion via Interval Analysis for Nonlinear Bounded-Error Estimation,” Automatica, 29(4), pp. 1053–1064. [CrossRef]
Johnson, T., and Tucker, W., 2008, “Rigorous Parameter Reconstruction for Differential Equations With Noisy Data,” Automatica, 44(9), pp. 2422–2426. [CrossRef]
Efimov, D., 2006, “Dynamical Adaptive Synchronization,” Int. J. Adapt. Control Signal Process., 20(9), pp. 491–507. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Zhang, Q., 2002, “Adaptive Observer for Multiple-Input-Multiple-Output Linear Time Varying Systems,” IEEE Trans. Autom. Control, 47(3), pp. 525–529. [CrossRef]
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.
Anderson, B. D. O., 1977, “Exponential Stability of Linear Equations Arising in Adaptive Identification,” IEEE Trans. Autom. Control, 22, pp. 83–88. [CrossRef]
Yuan, J. S.-C., and Wonham, W. M., 1977, “Probing Signals for Model Reference Identification,” IEEE Trans. Autom. Control, 22, pp. 530–538. [CrossRef]
Sanders, J., Verhulst, F., and Murdock, J., 2007, Averaging Methods in Nonlinear Dynamical Systems, Springer, New York.
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. [CrossRef]
Bogoliubov, N. N., and Mitropolskii, Yu, A., 1961, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York.
Blanke, M., Kinnaert, M., Lunze, J., and Staroswiecki, M., 2006, Diagnosis and Fault Tolerant Control, Springer-Verlag, Berlin, 2nd ed.
Chen, J., and Patton, R. J., 1999, Robust Model-Based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers, London.
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. [CrossRef]
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. [CrossRef]
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.
Ding, S. X., 2008, Model-Based Fault Diagnosis Techniques. Design Schemes, Algorithms, and Tools, Springer, Heidelberg, Berlin.
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. [CrossRef]
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.
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. [CrossRef] [PubMed]
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. [CrossRef]


Grahic Jump Location
Fig. 1

The structure scheme of the system (19)

Grahic Jump Location
Fig. 2

Simulation results with noise: output y and its reference yd ((a) and (b)); θ⌢o for o∈{m,M} ((c) and (d)); fault-indicating signals s and d ((e) and (g))




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