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Data-Based System Analysis and Control of Flat Nonlinear Systems.
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In this article, a data-based parametrization of all trajectories using only input-output data is proposed, which can be used to solve the output-matching control problems for the unknown system without explicitly identifying a model.Abstract:
Willems et al. showed that all input-output trajectories of a discrete-time linear time-invariant system can be obtained using linear combinations of time shifts of a single, persistently exciting, input-output trajectory of that system. In this paper, we extend this result to the class of discrete-time single-input single-output flat nonlinear systems. We propose a data-based parametrization of all trajectories using only input-output data. Further, we use this parametrization to solve the data-based simulation and output-matching control problems for the unknown system without explicitly identifying a model. Finally, we illustrate the main results with numerical examples.read more
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Journal ArticleDOI
Behavioral systems theory in data-driven analysis, signal processing, and control
Ivan Markovsky,Florian Dörfler +1 more
TL;DR: Data-driven analysis, signal processing, and control methods as mentioned in this paper can be broadly classified as implicit and explicit approaches, with the implicit approach being more robust to uncertainty and robustness to noise.
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Linear tracking MPC for nonlinear systems Part II: The data-driven case.
TL;DR: In this article, a data-driven MPC approach to control unknown nonlinear systems using only measured input-output data with closed-loop stability guarantees is presented. But this approach is limited to affine systems.
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Data-Driven Control of Nonlinear Systems: Beyond Polynomial Dynamics
TL;DR: This paper first derives a data-driven parametrization of unknown nonlinear systems with rational dynamics, then applies this approach to control systems whose dynamics are linear in general non-polynomial basis functions by transforming them into polynomial systems.
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Fundamental Lemma for Data-Driven Analysis of Linear Parameter-Varying Systems
TL;DR: In this article, the authors generalize the fundamental Lemma result of Willems et al. to linear time-invariant (LTI) systems and apply it to nonlinear systems.
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A Matrix Finsler's Lemma with Applications to Data-Driven Control
TL;DR: In this article, a matrix version of the classical Finsler's lemma has been shown to provide a tractable condition under which all matrix solutions to a quadratic equality also satisfy a quadrinomial inequality.
References
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Book ChapterDOI
The unfalsified control concept: A direct path from experiment to controller
TL;DR: The “unfalsified control” concept is introduced as a framework for determining control laws whose ability to meet given performance specifications is at least not invalidated by the available data.
Journal ArticleDOI
Data-based stabilization of unknown bilinear systems with guaranteed basin of attraction
TL;DR: For an unknown discrete-time bilinear system, the data collected in an offline open-loop experiment enable us to design a feedback controller and provide a guaranteed underapproximation of its basin of attraction.
Journal ArticleDOI
Canonical Forms for Nonlinear Systems
TL;DR: In this article, a survey of nonlinear scalar input and output systems with respect to controllability, observability, controller, and observer forms is presented, with a focus on nonlinear canonical (normal) forms.
Journal ArticleDOI
Conditions for the existence of a flat input
Steffen Waldherr,Michael Zeitz +1 more
TL;DR: The results provide a necessary and sufficient condition for the existence of a flat input in the SISO case, which also allows to construct of the vector field associated to the flat input.
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Data-driven Stabilization of SISO Feedback Linearizable Systems.
Paulo Tabuada,Lucas Fraile +1 more
TL;DR: The results in this paper provide sufficient conditions under which a modified version of Fliess and Join's approach is guaranteed to result in asymptotically stable behavior.
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