Closed-loop parameter identification of second-order non-linear systems: a distributional approach using delayed reference signals

This work presents a closed-loop parameter identification algorithm for a class of second-order non-linear systems affected by constant disturbances, quantisation, and state estimation errors. The proposed scheme permits obtaining a linear parameterisation of the non-linear system by developing a simplified procedure that allows using the distributional framework approach straightforwardly. The parametrisation stage requires signals with known delays. These delays are introduced to the system through the reference signal. Then, the linear parametrisation is used by a least-squares (LS) algorithm and a state estimator to generate the estimated values of the system parameters and the constant disturbance. The proposed algorithm is compared to a standard off-line LS algorithm in numerical simulations. Besides, the effectiveness and robustness of the proposed methodology are verified using a Monte Carlo simulation by considering that the system's output is corrupted by white noise. The results indicate that the proposed parameter identification scheme outperforms the LS algorithm, but without requiring any pre-processing stage.