Data-Driven Stabilization Using Prior Knowledge on Stabilizability and Controllability

TL;DR

This paper investigates how prior knowledge of stabilizability and controllability can improve data-driven stabilization of linear systems, leading to weaker conditions and new control design methods.

Contribution

It introduces a formal framework incorporating prior system-theoretic knowledge into data-driven stabilization, resulting in weaker conditions and new LMI-based control design methods.

Findings

Prior knowledge of controllability does not relax stabilization conditions.

Prior knowledge of stabilizability leads to necessary and sufficient weaker conditions.

New LMI-based control design methods are proposed.

Abstract

In this work, we study data-driven stabilization of linear time-invariant systems using prior knowledge of system-theoretic properties, specifically stabilizability and controllability. To formalize this, we extend the concept of data informativity by requiring the existence of a controller that stabilizes all systems consistent with the data and the prior knowledge. We show that if the system is controllable, then incorporating this as prior knowledge does not relax the conditions required for data-driven stabilization. Remarkably, however, we show that if the system is stabilizable, then using this as prior knowledge leads to necessary and sufficient conditions that are weaker than those for data-driven stabilization without prior knowledge. In other words, data-driven stabilization is easier if one knows that the underlying system is stabilizable. We also provide new data-driven control design methods in terms of linear matrix inequalities that complement the conditions for informativity.