Designing an Adaptive Fuzzy Extended State Observer for Nonlinear Affine Systems with External Disturbance

In this paper, an adaptive fuzzy extended state observer is proposed to estimate the states and external disturbances simultaneously for Single-Input-Single-Output nonlinear affine systems. The observer gains are time-varying and adjusted using an adaptive law. The Takagi-Sugeno fuzzy system is used for modeling that, unlike Mamdani methods, provides a more precise and comprehensive analysis. The proposed adaptive fuzzy observer is designed to relax the limitations of the extended state observers and improve system performance as compared to the classical methods in presence of time-varying disturbances. Moreover, the stability of the proposed method and the convergence of the estimation error are analyzed using the Lyapunov stability Theory. The performance of the proposed method is shown in simulations of control of the inverted pendulum. The simulation results, as compared to the non-adaptive fuzzy observer, show better performance in terms of transient and steady-state responses, control input amplitude, and robustness in presence of measurement noise and external disturbances.