Online system identification method using modified regularized exponential forgetting

Abstract

The paper deals with the use of regularized exponential forgetting (REF) in the process of online system identification. The deployment of this type of forgetting strategy is advantageous for very long runs with small changes in the identified input parameters (in the range of 100 000 steps). In these cases, the classical methods of forgetting, such as an exponential (EF) or directional forgetting (DF) lack the required quality and reach the limit of numerical stability of the calculations of system parameters, which may lead to the early termination of system identification procedure. To avoid this undesirable effect and maintain sufficient primary information about the identified system, a modified REF method is used that employs alternative covariance matrix (ACM) formulation to store the primary information of the identified system (REFACM) and prevents the numerical destabilization of the identification process. The quality of the modified REFACM forgetting method —along with its validation and comparison with REZ to verify its properties—is performed using standard tests.