Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness

In a paper by Willems et al., it was shown that persistently exciting data can be used to represent the input-output behavior of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems that paves the way to solve important control problems using data...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 65; no. 3; pp. 909 - 924
Main Authors De Persis, Claudio, Tesi, Pietro
Format Journal Article
LanguageEnglish
Published New York IEEE 01.03.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Control design
Data models
data-driven control
learning systems
Linear matrix inequalities
Linear quadratic regulator
Linear systems
Mathematical analysis
nonlinear control systems
Nonlinear systems
Output feedback
Parameterization
Robust control
Robustness
Stabilization
Trajectory
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Summary:In a paper by Willems et al., it was shown that persistently exciting data can be used to represent the input-output behavior of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems that paves the way to solve important control problems using data-dependent linear matrix inequalities only. The result is remarkable in that no explicit system's matrices identification is required. The examples of control problems we solve include the state and output feedback stabilization, and the linear quadratic regulation problem. We also discuss robustness to noise-corrupted measurements and show how the approach can be used to stabilize unstable equilibria of nonlinear systems.
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content type line 14
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2019.2959924