Using adaptive estimation approaches, a method is presented for the on
-line identification of hysteretic systems under arbitrary dynamic env
ironments. The availability of such an identification approach is cruc
ial for the on-line control and monitoring of nonlinear structural sys
tems to be actively controlled. In spite of the challenges encountered
in the identification of the hereditary nature of th restoring force
of such nonlinear systems, it is shown through the use of simulation s
tudies and experimental measurements that the proposed approach can yi
eld reliable estimates of the hysteretic restoring force under a very
wide range of excitation levels and response ranges.