Data-Driven Gain Scheduling Control of Linear Parameter-Varying Systems using Quadratic Matrix Inequalities

TL;DR

This paper introduces a data-driven gain scheduling control method for LPV systems using quadratic matrix inequalities, enabling stabilization of all plants consistent with measured data.

Contribution

It develops a novel approach employing quadratic matrix inequalities and vertex enumeration to synthesize controllers for LPV systems based on data.

Findings

Effective stabilization of LPV systems demonstrated

Method is computationally tractable

Applicable to systems with measured input/state data

Abstract

This paper synthesizes a gain-scheduled controller to stabilize all possible Linear Parameter-Varying (LPV) plants that are consistent with measured input/state data records. Inspired by prior work in data informativity and LTI stabilization, a set of Quadratic Matrix Inequalities is developed to represent the noise set, the class of consistent LPV plants, and the class of stabilizable plants. The bilinearity between unknown plants and `for all' parameters is avoided by vertex enumeration of the parameter set. Effectiveness and computational tractability of this method is demonstrated on example systems.