Adaptive observers in which parameters are updated infrequently

A hybrid model-reference adaptive observer (HMRAO) is introduced to eliminate some of the difficulties associated with conventional model-reference adaptive observers (MRAO). The HMRAO utilizes a periodic probing input and updates parameter estimates once per probing input period. The HMRAO is stable in the presence of controllable and observable unmodelled dynamics. Its adaptation convergence rates are inversely proportional to the eigenvalues of a symmetric matrix which can be computed on-line, and used to calculate the observer gain necessary to optimize the convergence rates. The HMRAO is a least-squares estimator, which leads to the frequency-domain interpretation that the estimated frequency response and the actual frequency response are matched most closely at the probing input frequencies. Identification experiments are performed on a flexible structure to test the stability, accuracy, convergence rates, tracking, and frequency-domain interpretation of the HMRAO.