Direct data-driven interpolation and approximation of linear parameter-varying system trajectories

TL;DR

This paper introduces a data-driven method for interpolating missing trajectory data in linear parameter-varying systems without relying on explicit parametric models, using conditions for solution existence and a direct algorithm.

Contribution

It presents a novel data-driven interpolation approach for shifted-affine LPV systems, including conditions for solution existence and a direct computational algorithm.

Findings

Applicable to mass-spring-damper systems with parameter variation

Provides conditions for solution existence and uniqueness

Demonstrates effectiveness through illustrative examples

Abstract

We consider the problem of estimating missing values in trajectories of linear parameter-varying (LPV) systems. We solve this interpolation problem for the class of shifted-affine LPV systems. Conditions for the existence and uniqueness of solutions are given and a direct data-driven algorithm for its computation is presented, i.e., the data-generating system is not given by a parametric model but is implicitly specified by data. We illustrate the applicability of the proposed solution on illustrative examples of a mass-spring-damper system with exogenous and endogenous parameter variation.