A variable forgetting factor RLS algorithm with application to fuzzy time-varying systems identification

A modified RLS-type adaptive algorithm with variable forgetting factor is introduced. The forgetting factor decreases or increases as the square of prediction error increases or decreases, and it converges to a constant less than one in the steady state, allowing the adaptive algorithm to track changes in the system automatically as well as produce a small steady-state error. The convergence of the algorithm is analysed. Simulation results are provided to support the analysis and to compare the performance of the modified algorithm with the constant forgetting factor RLS algorithm of Salgado et al. (1988) and the original variable for getting factor RLS algorithm of Fortescue et al. (1981). It is shown that the performance of the new algorithm compares favorably with these existing algorithms. Finally, the algorithm is applied to the identification of fuzzy time-varying systems, with satisfactory results.