LEAST-SQUARES TYPE ALGORITHMS FOR IDENTIFICATION IN THE PRESENCE OF MODELING UNCERTAINTY

The celebrated least squares and LMS (least-mean-squares) are system i dentification approaches that are easily implementable, need minimal a priori assumptions, and have very nice identification properties when the uncertainty in measurements is only due to noises and not due to unmodeled behavior of the system. When there is uncertainty present du e to unmodeled part of the system as well, however, the performance of these algorithms can be poor. Here we propose a ''modified'' weighted least squares algorithm that is geared toward identification in the p resence of both unmodeled dynamics and measurement disturbances. The a lgorithm uses very little a priori information and is easily implement able in a recursive fashion. Through an example we demonstrate the imp roved performance of the proposed approach. Motivated by a certain wor st-case property of the LMS algorithm, an H(infinity) estimation algor ithm is also proposed for the same objective of identification in the presence of modeling uncertainty.