# 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} }

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.

## 8 Citations

Koopman based data-driven predictive control

- Computer Science, EngineeringArXiv
- 2021

A novel data-driven simulation framework based on Wasserstein distance is designed, which outperforms the current formulation in dealing with uncertainty and is competitive to model-based method.

From System Level Synthesis to Robust Closed-loop Data-enabled Predictive Control

- Computer Science, EngineeringArXiv
- 2021

A robust closed-loop data-enabled predictive control scheme is proposed for stochastic LTI systems with a causal feedback structure, leading to an computational cost similar to standard robust MPC with full state measurements.

Behavioral systems theoryin data-driven analysis, signal processing, and control

- 2021

The behavioral approach to systems theory, put forward 40 years ago by Jan C. Willems, takes a representation-free perspective of a dynamical system as a set of trajectories. Till recently, it was an…

Near-Optimal Design of Safe Output Feedback Controllers from Noisy Data

- Computer Science, EngineeringArXiv
- 2021

This work forms a robustly safe version of the recently introduced Behavioral InputOutput Parametrization (BIOP) for the optimal predictive control of unknown constrained systems.

Robust Data-Enabled Predictive Control: Tractable Formulations and Performance Guarantees

- Computer Science, EngineeringArXiv
- 2021

It is shown that even though an accurate prediction of the future behavior is unattainable in practice due to inaccessibility of the perfect input/output data, the obtained robust optimal control sequence provides performance guarantees for the actually realized input/ Output cost.

A Behavioral Input-Output Parametrization of Control Policies with Suboptimality Guarantees

- Engineering, Computer ScienceArXiv
- 2021

A Behavioral version of the Input-Output Parametrization for the predictive control of unknown systems using output-feedback dynamic control policies is formulated, revealing, in a quantitative way, how the level of noise in the data affects the performance of behavioral methods.

Adaptive Robust Data-driven Building Control via Bi-level Reformulation: an Experimental Result

- Engineering, Computer ScienceArXiv
- 2021

This paper addresses the key noise-free assumption, and extends data-driven control schemes to adaptive building control with measured process noise and unknown measurement noise via a robust bilevel formulation, whose upper level ensures robustness and whose lower level guarantees prediction quality.

Linear tracking MPC for nonlinear systems Part II: The data-driven case

- Mathematics, Computer ScienceArXiv
- 2021

It is proved that this MPC scheme, which only requires solving strictly convex quadratic programs online, ensures that the closed loop converges to the (unknown) optimal reachable equilibrium that tracks a desired output reference while satisfying polytopic input constraints.

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