Quadric Inclusion Programs: an LMI Approach to H[infinity]-Model Identification

TL;DR

This paper introduces the Quadric Inclusion Program, a convex optimization method for identifying system models as norm-bounded inclusions from input-output data, with applications in robust control and noise mitigation.

Contribution

It presents a novel convex algorithm for system identification as frequency domain inclusions, with theoretical properties and noise mitigation strategies.

Findings

The algorithm effectively identifies system inclusions from data.

It offers a geometric interpretation of the inclusion fitting process.

The method outperforms least squares in data approximation tasks.

Abstract

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.