Data informativity for stabilization of discrete-time infinite-dimensional systems
Masashi Wakaiki
TL;DR
This work develops a data-driven informativity framework for stabilizing discrete-time infinite-dimensional systems using infinite-length data that form Bessel sequences. It derives necessary and sufficient conditions for informativity in the noise-free case (particularly for one-dimensional input) and provides a frame-based, noise-robust sufficient condition when the state data form a frame. The theory hinges on synthesis-operator ranges, density arguments, and operator inequalities, with a finite-length data extension under partial system knowledge that reduces the problem to a finite-dimensional subspace. The results yield explicit constructions of stabilizing gains and decay-rate bounds, and they illustrate the approach with a cascade heat equation example. Overall, the paper extends finite-dimensional informativity results to infinite-dimensional settings, offering practical criteria and computationally tractable conditions for data-driven stabilization.
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.