Data-driven Dissipativity Analysis of Linear Parameter-Varying Systems

TL;DR

This paper introduces a data-driven method for analyzing dissipativity in LPV systems using a single data sequence, employing semi-definite programming to verify system properties efficiently.

Contribution

It develops novel direct data-driven dissipativity analysis techniques for LPV systems, utilizing linear matrix inequalities and offering multiple implementation strategies.

Findings

Effective verification of dissipativity properties demonstrated in simulations

Methods exploit structural information like rate bounds for efficiency

Trade-offs between computational complexity and accuracy shown

Abstract

We derive direct data-driven dissipativity analysis methods for Linear Parameter-Varying (LPV) systems using a single sequence of input-scheduling-output data. By means of constructing a semi-definite program subject to linear matrix inequality constraints based on this data-dictionary, direct data-driven verification of $(Q,S,R)$-type of dissipativity properties of the data-generating LPV system is achieved. Multiple implementation methods are proposed to achieve efficient computational properties and to even exploit structural information on the scheduling, e.g., rate bounds. The effectiveness and trade-offs of the proposed methodologies are shown in simulation studies of academic and physically realistic examples.