Biased compensation adaptive gradient algorithm for rational model with time-delay using self-organising maps

This paper develops a biased compensation adaptive gradient decent algorithm for rational models with unknown time-delay. Owing to the unknown time-delay, traditional identification methods cannot be directly applied for such models. To overcome this difficulty, the self-organised maps are proposed, which can obtain the estimates of the time-delay based on the residual errors. Then, an adaptive gradient descent algorithm is introduced to obtain the parameter estimates. Compared with the traditional gradient descent and redundant rule based methods, the proposed method has two advantages: (1) each element in the parameter vector has its own step-size, thus it is more effective than the traditional gradient descent method; (2) the number of the unknown parameters is unchanged, therefore, it has less computational effort than the redundant rule based method. Finally, a simulation experiment is given to show the effectiveness of the proposed algorithm.