• Corpus ID: 231573142

Nonlinear Data-Enabled Prediction and Control

@article{Lian2021NonlinearDP,
  title={Nonlinear Data-Enabled Prediction and Control},
  author={Ying Zhao Lian and Colin Neil Jones},
  journal={ArXiv},
  year={2021},
  volume={abs/2101.03187}
}
  • Y. Lian, C. Jones
  • Published 8 January 2021
  • Computer Science, Mathematics, Engineering
  • ArXiv
The Willems’ fundamental lemma, which characterizes linear dynamics with measured trajectories, has found successful applications in controller design and signal processing, which has driven a broad research interest in its extension to nonlinear systems. In this work, we propose to apply the fundamental lemma to a reproducing kernel Hilbert space in order to extend its application to a class of nonlinear systems and we show its application in prediction and in predictive control. 

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References

SHOWING 1-10 OF 31 REFERENCES
Data-driven stabilization of nonlinear polynomial systems with noisy data
TLDR
This note extends the 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.
A trajectory-based framework for data-driven system analysis and control
TLDR
This paper translates the result from the behavioral context to the classical state-space control framework and extends it to certain classes of nonlinear systems, which are linear in suitable input-output coordinates, and shows how this extension can be applied to the data-driven simulation problem, where it introduces kernel-methods to obtain a rich set of basis functions.
Data-Enabled Predictive Control: In the Shallows of the DeePC
TLDR
The DeePC algorithm is shown to be equivalent to the classical and widely adopted Model Predictive Control (MPC) algorithm in the case of deterministic linear time-invariant systems and regularizations to the Dee PC algorithm are proposed.
Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
TLDR
This work extends the Koopman operator to controlled dynamical systems and applies the Extended Dynamic Mode Decomposition (EDMD) to compute a finite-dimensional approximation of the operator in such a way that this approximation has the form of a linearcontrolled dynamical system.
Neural network-based control design: an LMI approach
TLDR
A neural-network-based control design for a discrete-time nonlinear system with a multilayer perceptron of which the activation functions are of the sigmoid type symmetric to the origin and the stability of the closed-loop is guaranteed.
A note on persistency of excitation
We prove that if a component of the response signal of a controllable linear time-invariant system is persistently exciting of sufficiently high order, then the windows of the signal span the full
Learning Feature Maps of the Koopman Operator: A Subspace Viewpoint
TLDR
A new data-driven framework for learning feature maps of the Koopman operator by introducing a novel separation method that provides a flexible interface between diverse machine learning algorithms and well-developed linear subspace identification methods.
Virtual reference direct design method: an off-line approach to data-based control system design
TLDR
This paper presents a direct model-reference approach to the off-line design of linear controllers, suited to deal with plants described by a single set of open-loop I/O measurements only, which reduces to a standard identification problem.
Recurrent Neural Network based MPC for Process Industries
TLDR
This article combines data-driven modeling with MPC and investigates how to train, validate, and incorporate a special recurrent neural network (RNN) architecture into an MPC framework, designed for being scalable and applicable to a wide range of multiple-input multiple-output systems encountered in industrial applications.
System Identification: A Machine Learning Perspective
TLDR
This research presents a novel approach to estimating functions from sparse and noisy data that exploits Tikhonov regularization theory and its applications in reinforcement learning.
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