Finite Time Observers for Nonlinear System by Solving LMIs Problem: Application to the Manipulator Arm
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In this article, we consider the synthesis of finite time observers for some class of nonlinear systems by solving some LMI problem. First, we develop a method to calculate a constant gain which is used to determine an observer for a class of nonlinear systems. Secondly, we use an affine gain to synthesis the observer. The method can also be applied to the case of another class of nonlinear systems with nonlinear output. An application to the manipulator arm and a numerical example illustrate the proposed theory and point out the ameliorations comparing with asymptotic observers.
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A. Zemouche, “sur l’observation de l’état des systèmes dynamiques non linéaires,Thèse de Doctorat, Université Louis Pasteur Strasbour 1, France, 2007.
A. Zemouche, M. Boutayeb, and G. I. Bara. Observer design for nonlinear systems :An approach based on the differential mean value theorem. In 44th IEEE Conference on Decision and Control and European Control Conference CDC-ECC 2005, Seville, Spain, December 2005.
A. J. Krener and A. Isidori. Linearization by output injection and nonlinear observers. Systems and Control Letters, 3(1) :47–52, 1983.
B. L. Walcott, M. J. Corless, and S. H. Zak. Comparative study of nonlinear state observation techniques. Int. J. of Control, 45(6) :2109–2132, 1987.
C. Ben Njima, W. Ben Mabrouk, G. Garcia and H. Messaoud: “Finite-time stabilization of nonlinear systems by state feedback“, 8th International Multi-Conference on Systems, Signals & Devices (SSD 2011), 22-25 Mars 2011, Sousse-Tunisie.
C. Ben Njima, W. Ben Mabrouk, G. Garcia, H. Messaoud, Robust finite-time stabilization of nonlinear systems, (2011) International Review of Automatic Control (IREACO), 4 (3), pp. 362-369.
C. Ben Njima, W. Ben Mabrouk, G. Garcia and H. Messaoud: “Finite Time Stabilization of uncertain linear continuous time systems” , The 13th international conference on Sciences and Techniques of Automatic control & computer engineering , December 17-19, 2012, Monastir, Tunisia
E. A. Misawa and J. K. Hedrick. Nonlinear observers-a state of the art survey. ASME Journal of Dynamic Systems, Measurement, and Control, 111:344–352, 1989.
E. Moulay and W. Perruquetti, Lyapunov-based approach for finite time stability and stabilization, Proc of the 44th IEEE Conference on decision and control, and the european control conference 2005, Seville, Spain.
E. Moulay, Contribution à l’étude de la stabilité en temps fini et de la stabilisation, thèse de doctorat, école centrale de Lille, 2005.
F. Amato, M. Ariola, C. Cosentino and C.T. Abdallah, Application of finite-time stability concepts to control of ATM networks. 40th Allerton conference on communication, control and computers, July, 2002.
F. Amato, M. Ariola, C. Cosentino, C.T. Abdallah and P. Dorato. Necessary and sufficient condition for finite-time stability of linear systems. Proc of the American Control Conference, p. 4452-4456, Denver, Colorado, 2003.
F. Amato, M. Ariola and C. Cosentino, Finite-time stabilization via dynamic output feedback, Automatica 42. 337-342, 2006.
F. Amato, M. Ariola and P. Dorato. Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica 37(9):1459-1463, 2001.
F. E. Thau. Observing the state of nonlinear dynamic systems. Int. J. of Control, 17(3) :471–479, 1973.
F. Zhu. Observer-based synchronization of uncertain chaotic system and its application to secure communications. Chaos, Solitons and Fractals. Volume 40, Issue 5, Pages 2384-2391, 2009.
G. Garcia, S. Tarbouriech and J. Bernussou, Finite time stabilization of linear time-varying continuous systems, IEEE Trans. On Automatic control, vol 54, N.2, pp 364-369, 2009.
G. Chen. Approximate Kalman filtering. World Scientific series in approximations and decompositions, 1993.
L. Weiss and E.F. Infante, 1967, Finite time stability under perturbing forces and on product spaces. IEEE Trans. Auto. Contr, Vol. 12, p. 54-59.
T.L. Liao and N.S. Huang. An observer-based approach for chaotic synchronization with applications to secure communications. IEEE Trans. Circuits Syst. I, 46(9) :1144–1150,1999.
M. Grewal and A. Andrews. Kalman filtering : Theory and practice. Prentice Hall, 1993.
N. G. Chetaev, stability of motion (in russian), GITTL, Moscow, 1955 (English Translation: Oxford: Pergamon Press, 1961)
P. Dorato, An overview of finite-time stability. Book chapter (Current Trends in Nonlinear Systems and Control), Springerlink.
P. R. Pagilla and Y. Zhu. Controller and observer design for Lipschitz nonlinear systems. In IEEE American Control Conference ACC’04, Boston, Massachusetts, USA, July 2004.
S. Boyd and L. Vandenberghe. Convex optimization with engineering applications. Lecture Notes, Stanford University, Stanford, 2001.
W. Ben Mabrouk, “Contribution à L’étude de la stabilisation en Temps Fini des Systèmes Linéaires et Non Linéaires,Thèse de Doctorat, Ecole Nationale d’Ingénieures de Monastir, Université de Monastir, Tunisie,2010.
W. Ben Mabrouk, C. Ben Njima, H. Messaoud and G. Garcia, “Finite-time stabilization of nonlinear affine systems“, Journal Européen des Systèmes Automatisés, volume 44, n° 3/2010, p 327-343.
Ghasemi, R., Menhaj, M.B., Designing intelligent advanced controller for a class of large scale non-canonical nonlinear systems: Observer-based approach, (2011) International Review on Modelling and Simulations (IREMOS), 4 (6), pp. 3317-3326.
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