Quadric Inclusion Programs: an LMI Approach to H[infinity]-Model Identification
For control engineers, this provides a convex LMI-based approach to identify robust control models from data, though the improvement over existing methods appears incremental.
The paper introduces Quadric Inclusion Programs (QIP) as a convex optimization method for H-infinity model identification, which fits norm-bounded uncertainty models to frequency-domain data. The method is shown to compare favorably with a least-squares approach on simulated data, satisfying inclusion requirements while being outlier-sensitive by design.
Practical application of H[infinity] robust control relies on system identification of a valid model-set, described by a linear system in feedback with a stable norm-bounded uncertainty, which must explains all possible (or at least all previously measured) behavior for the control plant. Such models can be viewed as norm-bounded inclusions in the frequency domain, and this note introduces the "Quadric Inclusion Program" that can identify inclusions from input--output data as a convex problem. We prove several key properties of this algorithm and give a geometric interpretation for its behavior. While we stress that the inclusion fitting is outlier-sensitive by design, we offer a method to mitigate the effect of measurement noise. We apply this method to robustly approximate simulated frequency domain data using orthonormal basis functions. The result compares favorably with a least squares approach that satisfies the same data inclusion requirements.