An Adaptive Sliding-Mode Observer for a Class of Uncertain Nonlinear Systems

Héctor Ríos 1 Denis Efimov 2 Wilfrid Perruquetti 3, 4
4 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
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, i.e. 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 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 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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Héctor Ríos, Denis Efimov, Wilfrid Perruquetti. An Adaptive Sliding-Mode Observer for a Class of Uncertain Nonlinear Systems. International Journal of Adaptive Control and Signal Processing, Wiley, 2018, 32 (3), pp.511 - 527. ⟨10.1002/acs.2857⟩. ⟨hal-01889143⟩

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