# Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control

@article{Korda2018LinearPF, title={Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control}, author={Milan Korda and Igor Mezi{\'c}}, journal={Autom.}, year={2018}, volume={93}, pages={149-160} }

## 304 Citations

Koopman Model Predictive Control of Nonlinear Dynamical Systems

- Mathematics
- 2020

This chapter presents a class of linear predictors for nonlinear controlled dynamical systems and focuses in particular on model predictive control (MPC) and shows that MPC controllers designed in this way enjoy computational complexity of the underlying optimization problem comparable to that of MPC for a linear dynamical system with the same number of control inputs and the same dimension of the state space.

Koopman Operator Theory for Nonlinear Dynamic Modeling using Dynamic Mode Decomposition

- MathematicsArXiv
- 2021

A brief summary of the Koopman operator theorem for nonlinear dynamics modeling is provided and several data-driven implementations using dynamical mode decomposition (DMD) for autonomous and controlled canonical problems are analyzed.

Robust Tube-based Model Predictive Control with Koopman Operators-Extended Version

- Mathematics, EngineeringAutom.
- 2022

Koopman operator-based model reduction for switched-system control of PDEs

- MathematicsAutom.
- 2019

Data-driven feedback stabilization of nonlinear systems: Koopman-based model predictive control

- MathematicsInternational Journal of Control
- 2021

The proposed feedback control design remains completely data-driven and does not require any explicit knowledge of the original system, and due to the bilinear structure of the Koopman model, seeking a CLF is no longer a bottleneck for LMPC.

Koopman Lyapunov‐based model predictive control of nonlinear chemical process systems

- MathematicsAIChE Journal
- 2019

Funding information National Science Foundation, Grant/Award Number: CBET-1804407 Abstract In this work, we propose the integration of Koopman operator methodology with Lyapunov-based model…

Data-Driven Nonlinear Stabilization Using Koopman Operator

- Mathematics
- 2020

The proposed approach is data-driven and relies on the use of time-series data generated from the control dynamical system for the lifting of a nonlinear system in the Koopman eigenfunction coordinates to construct a finite-dimensional bilinear representation of a control-affine nonlinear Dynamical system.

Learning Koopman Operators for Systems with Isolated Critical Points

- Mathematics2019 IEEE 58th Conference on Decision and Control (CDC)
- 2019

This paper considers the convergence of discrete-time Koopman approximation error to the continuous-time error and shows both how this convergence occurs in general and how it can fail for systems with multiple isolated critical points.

Learning Data-Driven Stable Koopman Operators

- MathematicsArXiv
- 2020

A formula for the global error of general Koopman representations is derived and imposing stability constraints on the data-driven model is motivated to improve the approximation of nonlinear systems over a longer horizon.

A data-driven Koopman model predictive control framework for nonlinear flows

- Mathematics
- 2018

The Koopman operator theory is an increasingly popular formalism of dynamical systems theory which enables analysis and prediction of the nonlinear dynamics from measurement data. Building on the…

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