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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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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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Journal ArticleDOI
Data-Driven Model Predictive Control With Stability and Robustness Guarantees
TL;DR: The presented results provide the first (theoretical) analysis of closed-loop properties, resulting from a simple, purely data-driven MPC scheme, including a slack variable with regularization in the cost.
Journal ArticleDOI
Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness
Claudio De Persis,Pietro Tesi +1 more
TL;DR: In this paper, the authors derive a parametrization of linear feedback systems that paves the way to solve important control problems using data-dependent linear matrix inequalities only, which is remarkable in that no explicit system's matrices identification is required.
Journal ArticleDOI
Data-driven simulation and control
Ivan Markovsky,Paolo Rapisarda +1 more
TL;DR: An approach for computing a linear quadratic tracking control signal that circumvents the identification step is presented and the results are derived assuming exact data and the simulated response or control input is constructed off-line.
Journal ArticleDOI
On Differentially Flat Nonlinear Systems
TL;DR: In this paper, a differential field characterization of a class of dynamic feedback linearizable systems is given via the notion of differentially flat systems, where the linearizing dynamic feedback is obtained as an endogeneous dynamic feedback.
Proceedings ArticleDOI
Minimum-phase nonlinear discrete-time systems and feedback stabilization
TL;DR: The notion of zero dynamics and minimum phase for discrete time nonlinear systems is introduced and sufficient conditions are given for state feedback stabilization and full linearization via dynamic compensation.
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