A closed-loop optimal experimental design for online parameter identification approach is developed for nonlinear dynamic systems. The goal of the observer and the nonlinear model predictive control theories is here to perform online computation of the optimal time-varying input and to estimate the unknown model parameters online. The main contribution consists in combining Lyapunov stability theory with an existing closed-loop identification approach, in order to maximise the information content in the experiment and meanwhile to asymptotically stabilise the closed-loop system. To illustrate the proposed approach, the case of an open-loop unstable aerodynamic mechanical system is discussed. The simulation results show that the proposed algorithm allows to estimate all unknown parameters, which was not possible according to previous work, while keeping the closed-loop system stable.