A pessimistic approach to frequency domain model (in)validation

Model (In) validation has been extensively studied during the past decade, leading to efficient algorithms to establish whether some a priori information, typically a given model, uncertainty and noise description, is consistent with some observed experimental data. These algorithms are optimistic in the sense that a given description is considered to be not invalidated by the experimental data when there exists at least one pair (noise, uncertainty) that together with the nominal model can reproduce the observed data. Thus, they can substantially underestimate the size of the model uncertainty, leading to poor performance or even instability when this information is used to design a robust controller. To solve this difficulty, in this paper we take a pessimistic approach, where we seek the smallest ball such that the resulting model is invalidated by the experimental data for all uncertainties outside this ball. Thus, a robust controller designed using this information is guaranteed to stabilize the unknown plant. The main result of the paper provides an LMI-based optimization procedure for computing an upper bound on the radius of this ball for the case of structured uncertainty entering the plant in an LFT form. Moreover, in the case of up to two uncertainty blocks this upper bound is indeed exact.