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arXiv · 2206.08408

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

Henk J. van Waarde·Jaap Eising·M. Kanat Camlibel·Harry L. Trentelman
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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 input-output 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.

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Henk J. van Waarde, Jaap Eising, M. Kanat Camlibel, Harry L. Trentelman. 2022-06-16. A behavioral approach to data-driven control with noisy input-output data. https://arxiv.org/abs/2206.08408

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