# Identification of Crude Distillation Unit: A Comparison between Neural Network and Koopman Operator
## 2 Modeling and Methodology
### Koopman Operator Theory
[CrossRef]
* [PERSON] (1931) [PERSON] Hamiltonian systems and transformation in hilbert space. _Proc. Natl. Acad. Sci. USA_**1931**, _17_, 315-318. [PubMed] [CrossRef]
* [PERSON] and [PERSON] (2004) [PERSON]; [PERSON] Comparison of systems with complex behavior. _Phys. D Nonlinear Phenom._**2004**, _197_, 101-133. [CrossRef]
* [PERSON] (2005) [PERSON] Spectral properties of dynamical systems, model reduction and decompositions. _Nonlinear Dyn._**2005**, _41_, 309-325. [CrossRef]
* [PERSON] and [PERSON] (2022) [PERSON]; [PERSON] [PERSON] Stable deep koopman model predictive control for solar parabolic-trough collector field. _Renen. Energy_**2022**, _198_, 492-504. [CrossRef]
* [PERSON] and [PERSON] (2011) [PERSON]; [PERSON] [PERSON] Nonlinear koopman modes and coherency identification of coupled swing dynamics. _IEEE Trans. Power Syst._**2011**, _26_, 1894-1904. [CrossRef]
* [PERSON] et al. (2017) [PERSON]; [PERSON]; [PERSON] Model-based control using koopman operators. _arXiv_**2017**, arXiv:1709.01568. * [PERSON] et al. (2022) [PERSON]; [PERSON]; [PERSON] Autonomous driving using linear model predictive control with a koopman operator based bilinear vehicle model. _IFAC-PapersOnLine_**2022**, _55_, 254-259. [CrossRef]
* [PERSON] (2017) [PERSON]; [PERSON] Pulse-based control using koopman operator under parametric uncertainty. _arXiv_**2017**, arXiv:1708.00232. [PERSON] (2020) [PERSON]; [PERSON] [PERSON] Data-driven analysis and forecasting of highway traffic dynamics. _Nat. Commun._**2020**, _11_, 2090. [CrossRef] [PubMed]
* [PERSON] (1989) [PERSON] _Models for Linear and Nonlinear Systems_; John Wiley & Sons, Ltd.: Hoboken, NJ, USA, 2013; Chapter 2, pp. 17-59. * [PERSON] et al. (1989) [PERSON]; [PERSON]; [PERSON] Multilayer feedforward networks are universal approximators. _Neural Netw._**1989**, \(2\), 359-366. [CrossRef]
* [PERSON] et al. (2018) [PERSON] [PERSON]; [PERSON]; [PERSON]; [PERSON] Modelling and control of greenhouse system using neural networks. _Trans. Inst. Meas. Control._**2018**, _40_, 918-929. [CrossRef]
* [PERSON] and [PERSON] (2019) [PERSON]; [PERSON] [PERSON] Identification of realistic distillation column using hybrid particle swarm optimization and NARX based artificial neural network. _Evol. Syst._**2019**, _10_, 149-166. [CrossRef]
* [PERSON] et al. (2020) [PERSON]; [PERSON]; [PERSON]; [PERSON] Prediction of the droplet spreading dynamics on a solid substrate at irregular sampling intervals: Nonlinear auto-regressive exogenous artificial neural network approach (narx-ann). _Chem. Eng. Res. Des._**2020**, _156_, 263-272. [CrossRef]
* [PERSON] et al. (2023) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] On the design of narx-anns for the black-box modeling of power electronic converters. In Proceedings of the 2023 IEEE Energy Conversion Congress and Exposition (ECCE), Nashville, TN, USA, 29 October-2 November 2023; pp. 2776-2782. * [PERSON] et al. (2020) [PERSON]; [PERSON]; [PERSON] (Eds.) _The Koopman Operator in Systems and Control: Concepts, Methodologies, and Applications_; Lecture Notes in Control and Information Sciences; Springer International Publishing: Cham, Switzerland, 2020; Volume 484. * [PERSON] et al. (2018) [PERSON] [PERSON]; [PERSON]; [PERSON] [PERSON] Generalizing koopman theory to allow for inputs and control. _Appl. Dyn. Syst._**2018**, _17_, 909-930. [CrossRef]
* [PERSON] et al. (2018) [PERSON]; [PERSON]; [PERSON]; [PERSON] Decomposition of nonlinear dynamical systems using koopman gramians. In Proceedings of the 2018 Annual American Control Conference (ACC), Milwaukee, WI, USA, 27-29 June 2018; pp. 4811-4818. * [PERSON] (2016) [PERSON] Koopman operator based observer synthesis for control-affine nonlinear systems. In Proceedings of the 2016 IEEE 55 th Conference on Decision and Control (CDC), Las Vegas, NV, USA, 12-14 December 2016; pp. 6492-6499. * [PERSON] and [PERSON] (2017) [PERSON]; [PERSON] Global bilinearization and controllability of control-affine nonlinear systems: A Koopman spectral approach.