Data informativity for stabilization of discrete-time infinite-dimensional systems

TL;DR

This paper presents a data-driven approach for stabilizing discrete-time infinite-dimensional systems, establishing conditions under which available data can guarantee the existence of a stabilizing feedback gain.

Contribution

It introduces new criteria for data informativity in infinite-dimensional systems, including noise considerations and finite-dimensional unstable parts.

Findings

Sufficient condition for data informativity in noise-free case

Necessary and sufficient conditions when the input space is one-dimensional

Extension of conditions to noisy data with frame assumptions

Abstract

This paper develops a data-driven framework for stabilization of discrete-time infinite-dimensional systems. We investigate informativity for stabilization, defined as the existence of a feedback gain that stabilizes all systems compatible with the available input-state data. Assuming that infinite-length data are Bessel sequences, we first establish a sufficient condition for data informativity in the noise-free case. We next show that this sufficient condition is also necessary under a mild data assumption when the input space is one-dimensional. Furthermore, if the state sequence forms a frame, then the sufficient condition can be extended to the case of noisy data. Finally, when the unstable part of the true system is known to be finite-dimensional, we derive a necessary and sufficient condition for data informativity of finite-length data.