Learning the Integral Quadratic Constraints on Plant-Model Mismatch

TL;DR

This paper introduces a data-driven method to learn integral quadratic constraints (IQCs) for plant-model mismatch using OC-SVM, enabling accurate characterization of uncertainties in nonlinear and delay systems.

Contribution

The paper proposes a novel OC-SVM-based approach to learn IQCs from data, providing a statistical analysis of its generalization performance for robust control.

Findings

Successfully applied to time delay mismatch and nonlinear reactor systems.

Achieved accurate recovery of frequency-domain uncertainties.

Demonstrated effectiveness in capturing plant-model mismatches.

Abstract

While a characterization of plant-model mismatch is necessary for robust control, the mismatch usually can not be described accurately due to the lack of knowledge about the plant model or the complexity of nonlinear plants. Hence, this paper considers this problem in a data-driven way, where the mismatch is captured by parametric forms of integral quadratic constraints (IQCs) and the parameters contained in the IQC equalities are learned from sampled trajectories from the plant. To this end, a one-class support vector machine (OC-SVM) formulation is proposed, and its generalization performance is analyzed based on the statistical learning theory. The proposed approach is demonstrated by a single-input-single-output time delay mismatch and a nonlinear two-phase reactor with a linear nominal model, showing accurate recovery of frequency-domain uncertainties.