A convex optimization approach to model (in)validation of switched ARX systems with unknown switches

Abstract

This paper considers the problem of (in)validating switched affine models from noisy experimental data, in cases where the mode-variable is not directly observable. This problem, the dual of identification, is a crucial step when designing controllers using models identified from experimental data. Our main results are convex certificates, obtained by exploiting a combination of sparsification and polynomial optimization tools, for a given model to either be consistent with the observed data or be invalidated by it. These results are illustrated using both academic examples and a non-trivial application: detecting abnormal activities using video data.