Convex behavioral model (in)validation via Jensen-Bregman divergence minimization

This paper considers the problem of determining whether two pairs of (noisy) time sequences (u; y) are behaviors of the same (unknown) underlying system. That is, whether these pairs are admissible input/output trajectories for some suitable initial condition. This problem is relevant to many practical scenarios arising not only in the context of control and systems identification, e.g. model (in)validation and fault detection, but also in other fields, including computer vision and image processing. Our main result shows that this problem can be reduced to minimizing the Jensen-Bregman logdet divergence between two suitable constructed Grammian matrices, a problem that can be efficiently solved using recently introduced methods. This result is illustrated with two non-trivial examples: activity recognition from video sequences and fault detection in a bearing rig.