Convergence Analysis of Forgetting Factor Least Squares Algorithm for ARMAX Time-Delay Models.

In this paper, the estimation problem is considered for both sample delay and coefficients of ARMAX model. An extended recursive least squares algorithm is derived by minimizing a quadratic cost function. However, the solution of the optimization problem returns a real value for the sample delay. To overcome this difficulty, the rounding properties are used to transform the integer nonlinear problem into a real optimization problem. In addition, consistency of the estimates with their convergence rates are established under the persistent excitation condition. Finally, experimental results on semi-batch reactor are presented to illustrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]