Model (In)validation and Fault Detection for Systems with Polynomial State-Space Models

This paper addresses the problem of (in) validation of polynomial state-space models, that is, checking whether a discrete-time uncertain polynomial state-space model can explain noisy experimental input/output data. We first recast this problem as a polynomial optimization problem and present asymptotically tight invalidation certificates by appealing to well-known moments-based relaxations. In the second part of the paper, we show how a model-based run-time fault detection algorithm can be developed based on a notion of T -detectability, which enables the proposed model invalidation approach to be applied in receding horizon fashion to detect faults. The efficacy of the proposed methods are illustrated with some numerical and practical examples.