This paper is focused on the design of a robust model based extremum-seeking controller (ESC) aimed at the online optimization of a class of uncertain nonlinear systems. The ESC scheme is based on the modeling-error compensation approach using a robust input-output linearizing control law coupled with a first-order gradient estimator. The feedback control scheme is able to drive the closed-loop system into a vicinity of the optimal operating set-point In contrast with perturbation-based ESC algorithms, the control scheme includes an observer-based uncertain estimator for computing unknown components related to model uncertainties and a continuous gradient estimator, while avoiding the use of a perturbation signal for achieving closed-loop convergence to the optimal neighborhood. The convergence of the closed-loop system to the unknown optimal set-point is analyzed. Numerical simulations illustrate the effectiveness of the proposed ESC scheme in two different nonlinear systems. (C) 2019 Elsevier Ltd. All rights reserved.