A behavioral approach to data-driven control with noisy input-output data

Abstract

This paper deals with data-driven stability analysis and feedback stabillization of linear input-output systems in autoregressive (AR) form. We assume that noisy input-output data on a finite time-interval have been obtained from some unknown AR system. Data-based tests are then developed to analyse whether the unknown system is stable, or to verify whether a stabilizing dynamic feedback controller exists. If so, stabilizing controllers are computed using the data. In order to do this, we employ the behavioral approach to systems and control, meaning a departure from existing methods in data driven control. Our results heavily rely on a characterization of asymptotic stability of systems in AR form using the notion of quadratic difference form (QDF) as a natural framework for Lyapunov functions of autonomous AR systems. We introduce the concepts of informative data for quadratic stability and quadratic stabilization in the context of inputoutput AR systems and establish necessary and sufficient conditions for these properties to hold. In addition, this paper will build on results on quadratic matrix inequalties (QMIs) and a matrix version of Yakubovich's S-lemma.

When sampling works in data-driven control: Informativity for stabilization in continuous time

“…In this case, the fact that w is L-square Lipschitz with L = 16 (alternatively, a more conservative bound for L could be obtained from Lemma IV.10). Note in particular that the set inclusions displayed in Figure 2, where Z(N cont (1)) is contained in each of the sets Z N δ (1 + 1 2 δT L) , are consistent with (15) in Corollary IV.7.…”

From data to reduced-order models of complex dynamical systems

“…Firstly, since the current result only works with single input single output (SISO) systems as well as SISO data, an interpolatory method for multi input multi output (MIMO) systems on the basis of MIMO data might be developed by using data informativity for tangential interpolation. To deal with MIMO data, one might refer to the kernel representation used in [184]. In this case, an updated definition of moments needs to be formulated.…”

“…The use of quadratic differential or difference forms proposed in [192] to analyze dissipativity from such data is a promising direction to obtain reduced-order models within the informativity approach in these chapters. Some existing results related to this idea can be found in [150,184].…”