Determination of Set-Membership Identifiability Sets

This paper concerns the concept of set-membership identifiability introduced in Jauberthie et al. (Proceedings of the 18th IFAC World Congress. Milan, Italie, 12024–12029, 2011). Given a model, a set-membership identifiable set is a connected set in the parameter domain of the model such that its corresponding trajectories are distinct to trajectories arising from its complementary. For obtaining the so-called set-membership identifiable sets, we propose an algorithm based on interval analysis tools. The proposed algorithm is decomposed into three parts namely mincing, evaluating and regularization (Jaulin et al. in Applied interval analysis, with examples in parameter and state estimation, robust control and robotics. Springer, Londres, 2001). The latter step has been modified in order to obtain guaranteed set-membership identifiable sets. Our algorithm will be tested on two examples.