An adaptive sliding‐mode observer for a class of uncertain nonlinear systems |
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Authors: | H. Ríos D. Efimov W. Perruquetti |
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Affiliation: | 1. CONACYT ‐TECNM/División de Estudios de Posgrado e Investigación, Instituto Tecnológico de La Laguna, 27000 Torreón, Coahuila, México;2. Non‐A Team at Inria, Parc Scientifique de la Haute Borne, 59650 Villeneuve d'Ascq, France;3. CRIStAL, Ecole Centrale de Lille, UMR 9189 CNRS, 59651 Villeneuve d'Ascq, France;4. Department of Control Systems and Informatics, Information Technologies Mechanics and Optics University, Saint Petersburg 197101, Russia |
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Abstract: | In this paper, the problem of simultaneous state and parameter estimation is studied for a class of uncertain nonlinear systems. A nonlinear adaptive sliding‐mode observer is proposed based on a nonlinear parameter estimation algorithm. It is shown that such a nonlinear algorithm provides a rate of convergence faster than exponential, ie, faster than the classic linear algorithm. Then, the proposed parameter estimation algorithm is included in the structure of a sliding‐mode state observer, providing an ultimate bound for the full estimation error and attenuating the effects of the external disturbances. Moreover, the synthesis of the observer is given in terms of linear matrix inequalities. The corresponding proofs of convergence are developed based on the Lyapunov function approach and input‐to‐state stability theory. Some simulation results illustrate the efficiency of the proposed adaptive sliding‐mode observer. |
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Keywords: | adaptive observer nonlinear systems sliding‐modes |
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