LMI-based strategies for designing observers and unknown input observers for non-linear discrete-time systems

• Autorzy: Korbicz J. , Witczak M. , Puig V.
• Języki publikacji: EN

Abstrakty

EN

The paper deals wit h the problems of designing observers and unknown input observers for discrete-time Lipschitz non-linear systems. In particular, with the use of the Lyapunov method, three different convergence criteria of the observer are developed. Based on the achieved results, three different design procedures are proposed. Then, it is shown how to extend the proposed approach to the systems with unknown inputs. The final part of the paper presents illustrative examples that confirm the effectiveness of the proposed tech-niques. The paper also presents a MATLAB@ function that implements one of the design procedures.

Słowa kluczowe

EN

non-linear systems; state estimation; observes; fault diagnosis; convergence; LMI

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2007
• Tom: Vol. 55, nr 1
• Strony: 31--42
• Opis fizyczny: Bibliogr. 36 poz., rys.

Twórcy

autor

Korbicz J.

autor

Witczak M.

autor

Puig V.

• Institute of Control and Computation Engineering, University of Zielona Góra, 50 Podgórna, 65-246 Zielona Góra, Poland,,

Bibliografia

• [1] J. Korbicz, J.M. Kościelny, Z. Kowalczuk, and W. Cholewa, Fault Diagnosis. Models, Artificial Intelligence, Applications, Springer- Verlag, Berlin 2004.
• [2] J. Chen and R J. Patton, Robust Model-based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers, London, 1999.
• [3] F. Delebecque, R Nikoukah, and H. Rubio Scala, "Test signal design for failure detection: a linear programming approach", Int. J. Appl. Math. Comput. Sci. 13 (4), 515-526 (2003).
• [4] Z. Kowalczuk and T. Bialaszewski, "Niching mechanisms in evolutionary computation", Int. J. Appl. Math. Comput. Sci. 16 (1), 59-84 (2006).
• [5] E. Alcorta Garcia and P.M. Frank, "Deterministic nonlinear observer-based approaches to fault diagnosis", Control. Eng. Practice 5 (5), 663-670 (1997).
• [6] C. Califano, S. Monaco, and D. Normand-Cyrot, "On the observer design in discrete-time", System and Control Letters 49, 255-265 (1997).
• [7] M. Witczak, A. Obuchowicz, and J. Korbicz, "Genetic programming based approaches to identification and fault diagnosis of non-linear dynamic systems", Int. J. Contr. 75 (13),1012-1031 (2002).
• [8] M. Witczak, Identification and Fault Detection of Nonlinear Dynamic Systems, University of Zielona Góra Press, Zielona Góra, 2003.
• [9] R. Seliger and P. Frank, "Robust observer-based fault diagnosis in non-linear uncertain Systems", in Issues of Fault Diagnosis for Dynamic Systems, edited by R J. Patton, P. Frank, and R. N. Clark, Springer-Verlag, Berlin, 2000.
• [10] S.H. Wang, E.J. Davison, and P. Dorato, "Observing the states of systems with unmeasurable disturbances", IEEE Trans. Automatic Control 20 (5),716-717 (1975).
• [11] S.P. Bhattacharyya, "Observer design for linear systems wit h unknown inputs", IEEE Trans. Automat. Contr. 23 (3),483-484 (1978).
• [12] N. Kobayashi and R Nakamizo, "An observer design for linear systems wit h unknown inputs", Int. J. Contr. 17 (3),471-479 (1982).
• [13] M. Hou and P.C. Müller, "Design of observers for linear systems with unknown inputs", IEEE Trans. Automatic Control 37 (6),871-875 (1992).
• [14] J. Chen, R J. Patton, and H. Zhang, "Design of unknown input observers and fault detection filters" - Int. J. Contr. 63 (1),85-105 (1996).
• [15] S. Hui, S.H. Zak, "Observer design for systems with unknown input", Int. J. Appl. Math. Comput. Sci. 15 (4), 431-446 (2005).
• [16] M. Darouach and M. Zasadzinski, "Unbiased minimum variance estimation for systems with unknown exogenous in.puts", Automatica 33 (4), 717-719 (1997).
• [17] M. Hou and RJ. Patton, "Optimal filtering for systems with unknown inputs", IEEE Trans. Automatic Control 43 (3), 445-449 (1998).
• [18] J. Y. Keller and M. Darouach, "Two-stage Kalman estimator with unknown exogenous inputs", Automatica 35, 339-342 (1999).'
• [19] D. Maksarov and .J. Norton, "State bounding with ellipsoidal set description of the uncertainty" Int. J. of Control 65 (5), 847-866 (1996).
• [20] S.A. Ashton, D.N. Shields, and S. Daley, "Design of a robust fault detection observer for polynomial nonlinearities", Proc. 14th IFAC World Congress, Beijing, China, CD-ROM (1999).
• [21] A. Hac, "Design of disturbance decoupled observers for bilinear systems", ASME J. Dynamic Sys. Measure. Contr. 114, 556-562 (1992).
• [22] D. Koenig and S. Mammar, "Design of a class of reduced unknown inputs non-linear observer for fault diagnosis", Proc. American Control Conference, Arlington, USA, CD-ROM (2001).
• [23] A.M. Pertew, H.J. Marquez, and Q. Zhao, "Design of unknown input observers for Lipschitz non-linear systems", Proc. American Control Conference, Portland, USA, CD-ROM (2005).
• [24] A. Zolghardi, D. Henry, and M. Monision, "Design of nonlinear observers for fault diagnosis. A case study", Control. Eng. Practice 4 (11), 1535-1544 (1996).
• [25] M. Boutayeb and D. Aubry, "A strong tracking extended Kalman observer for non-linear discrete-time systems", IEEE Trans. Automat. Contr. 44 (8),1550-1556 (1999).
• [26] Y. Song and J.W. Gizzle, "The extended Kalman filter as a local asymptotic observer for non-linear discrete-time systems", J. Math., Estimation, Contr. 5, 59-78 (1995).
• [27] F.E. Thau, "Observing the state of non-linear dynamic systems", Int. J. Contr 17 (3), 471-479 (1973).
• [28] G. Schreier, J. Ragot, RJ. Patton, and P.M. Frank, "Observer design for a class of non-linear systems", IFAC Symp.: Fault Detection, Supervision and Safety of Technical Processes: SAFEPROCESS'97 1, 483-488 (1997).
• [29] C. Aboky, G. Sallet, and J.C. Vivalda, "Observers for Lipschitz non-linear systems", Int. J. Contr. 75, (3), 204-212, (2002).
• [30] R. Rajamani and Y.M. Cha, "Existence and design of observers for non-linear systems: relation to distance to unobservability", Int. J. Contr. 69 (5), 717-731 (1998).
• [31] R Rajamani, "Observers for Lipschitz non-linear systems", IEEE Trans. Aut. Control 43 (3),397-401 (1998).
• [32] K. Busawon, M. Saif, and M. Farza, "A discrete-time observer for a class of non-linear systems", 36th IEEE Conference on Decision and Control, 4796-4801 (1997).
• [33] Z. Wang and H. Unbehauen "A class of non-linear observers for discrete-time systems with parametric uncertainty", Int. J. Sys. Sci. 31 (1), 19-26 (2000).
• [34] H.G. Chen and KW. Han, "Improved quantitative measures of robustness for multivariable systems", IEEE Trans. Automatic Control 39 (4),807-810 (1994).
• [35] S. Boyd, E. Feron, L.E. Ghaoui, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Siam, Philadelphia, 1994.
• [36] P. Gahinet, A. Nemirovski, A.J. Laub, and M. Chilali, LMI Control Toolbox. For Use with Matlab, MathWorks Inc., Natick, 1995.