Matching a system behavior with a known set of models: A quadratic optimization-based adaptive solution

The matching process between a time-domain external behavior of a lumped single-input single-output dynamical system and a known set of linear continuous time-invariant models is tackled in this paper. The proposed online solution is based on an adaptive structure detector, which in finite time locates in the known set of models the one corresponding to the observed external behavior; the detector results from the solution of a constrained quadratic optimization problem. The problem is expressed in terms of the time-domain activity of a family of discriminating filters and is solved via a normalized gradient algorithm, which avoids mismatching due to the presence of structural zeros in the filters and can take into account band-limited high-frequency measurement noise. A failure detection problem concerning a simulated servomechanism is included in order to illustrate the proposed solution.