An adaptive observer for a class of nonlinear systems with a high-gain approach. Application to the twin-rotor system

Habib Dimassi (1) , Salim Hadj Saïd (2) , Antonio Loria (1) , Faouzi M'Sahli (2)

1 L2S - Laboratoire des signaux et systèmes
2 ENIM - École Nationale d’Ingénieurs de Monastir

In this paper, we investigate the problem of adaptive observer design for a class of non-linear systems subject to unknown parameters and such that the classical observer matching assumption is not satisfied. That is, it is assumed that the relative degree of the outputs with respect to the unknown parameters vector is at least equal to two. We adopt the idea of generating auxiliary outputs based on a high gain observer. The generated outputs are employed by a new adaptive observer to reconstruct both the states and unknown parameters. The stability analysis of the system error is established based on a Lyapunov analysis. It is shown that the state estimation error and the adaptation error are uniformly bounded and converge to a compact set that may be reduced by an appropriate choice of the design parameters. In order to improve the robustness of our approach, the proposed adaptive observer is appropriately modified based on sliding modes theory to compensate for the effect of the time-varying and bounded disturbances. Theoretical results are illustrated and validated for the twin rotor MIMO system with numerical simulations.

Mots clés: Adaptive observer; high gain observers; observer matching condition; unknown parameters; twin rotor MIMO system

Domaines: Automatique

Habib Dimassi, Salim Hadj Saïd, Antonio Loria, Faouzi M'Sahli. An adaptive observer for a class of nonlinear systems with a high-gain approach. Application to the twin-rotor system. International Journal of Control, 2021, 94 (2), pp.370-381. ⟨10.1080/00207179.2019.1594387⟩. ⟨hal-02367534⟩