Open AccessPosted Content
Data-Based System Analysis and Control of Flat Nonlinear Systems.
TLDR
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
Citations
More filters
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.
Posted Content
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.
Posted Content
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.
Posted Content
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.
Posted Content
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
More filters
Proceedings ArticleDOI
Data-Driven Internal Model Control of Second-Order Discrete Volterra Systems
TL;DR: In this paper, the data-driven approach is extended to a class of nonlinear systems, namely second-order discrete Volterra systems, and two main contributions are made for this class of systems.
Posted Content
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.
Journal ArticleDOI
Data-driven stabilization of nonlinear polynomial systems with noisy data
TL;DR: In this article, the authors extend this approach to deal with unknown nonlinear polynomial systems by formulating stability certificates in the form of data-dependent sum of squares programs, whose solution directly provides a stabilizing controller and a Lyapunov function.
Proceedings ArticleDOI
Some comments about linearization under sampling
TL;DR: In this paper, a digital control strategy for achieving partial linearization at a fixed order of approximation is proposed, considering the sampled dynamics as a system which is regularly perturbed by the sampling period delta.
Posted Content
Data-Driven Stabilization of Nonlinear Systems with Rational Dynamics.
TL;DR: This paper presents a data-driven controller design method for continuous-time nonlinear systems with rational system dynamics, using no model knowledge but only measured data affected by noise, and obtains sum-of-squares based criteria for designing controllers with closed-loop robust stability guarantees.
Related Papers (5)
Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness
Claudio De Persis,Pietro Tesi +1 more