An on-line modified least-squares identification algorithm is proposed for linear time-varying systems with bounded disturbances under relaxed excitation conditions. An extra term which enhances the tracking ability for time-varying parameters is added to the covariance's update law. An indicator of the regressor's excitation level based on the maximum eigenvalue of the covariance matrix is developed. By combining the maximum eigenvalue with its variation trend shown by the sensitivity of the maximum eigenvalue to change in the covariance matrix, a novel identification law, which is switched between a modified least-squares algorithm and a gradient algorithm based on fixed σ-modification, is proposed. The boundedness of the estimation error and the covariance matrix are guaranteed via Lyapunov stability theory. The superiority of the proposed method is verified by simulations. INDEX TERMS Least-squares identification algorithms, linear time-varying systems, relaxed excitation conditions, covariance matrix.

No abstract

No abstract

No abstract

Identification of time delay is a prerequisite for the realisation of control compensation. The existing researches generally assume that the system input should be monotonic, which is unsuitable for online identification due to system saturation. To solve this problem, relaxed input conditions are developed in this Letter. Then a modified least‐square algorithm with forgetting factors, which has a strong ability in tracking time‐varying delays, is presented. Meanwhile, two extra terms whose design parameters are adjusted online according to the input condition are added into the covariance update law to guarantee the boundedness and robustness of the algorithm. Simulation results demonstrate the superiority of the proposed method and the reasonableness of the developed input conditions.