Data-based Transfer Stabilization in Linear Systems

TL;DR

This paper introduces a transfer stabilization framework for linear systems that leverages abundant source data and limited target data, using LMIs to design controllers that stabilize a set of possible target systems.

Contribution

It proposes a novel data-driven transfer stabilization method for linear systems, incorporating source data and system proximity knowledge to efficiently design stabilizing controllers.

Findings

The method effectively stabilizes systems using source data and system proximity.

Feasibility conditions for the LMIs are thoroughly analyzed.

Numerical case studies demonstrate the approach's practicality.

Abstract

We present a novel framework for transferring the knowledge from one system (source) to design a stabilizing controller for a second system (target). Our motivation stems from the hypothesis that abundant data can be collected from the source system, whereas the data from the target system is scarce. We consider both cases where data collected from the source system is noiseless and noisy. For each case, by leveraging the data collected from the source system and a priori knowledge on the maximum distance of the two systems, we find a suitable, and relatively small, compact set of systems that contains the actual target system, and then provide a controller that stabilizes the compact set. In particular, the controller can be obtained by solving a set of linear matrix inequalities (LMIs). Feasibility of those LMIs is discussed in details. We complement our theoretical findings by two numerical case studies of low-order and high-order systems.