# KoopmanMPC_for_flowcontrol
This project demonstates the application of Koopman-MPC framework for flow control,
following the paper
*"A data-driven Koopman model predictive control framework for nonlinear flows"*
by H. Arbabi, M. Korda and I. Mezic (https://arxiv.org/pdf/1804.05291.pdf).
The Koopman-MPC framework is summarized in the below figure:
<img src="https://github.com/arbabiha/KoopmanMPC_for_flowcontrol/blob/master/thehood/BigPic.png" width="700">
### files in the root folder:
#### BurgersExample
Runs the Burgers example as explained in the paper, it includes data collection, Extended Dynamic Mode Decomposition (EDMD) for identification of the Koopman linear system, and a run of closed-loop controlled system from some initial condition.
Feel free to play with the paremeters of the code, specially, try different observables, embedding dimension, reference signal, initial condition, etc.
The whole program, with the initial paremeter settings, runs on my personal laptop in under 2 minutes.
#### CavityExample
Runs the lid-driven cavity flow example as explained in the paper, including EDMD for identification of the Koopman linear system, and a run of closed-loop controlled system from some initial condition on the limit cycle. There are two options to run this code:
1- ask the code to generate data for EDMD. This is a lengthy process and for the parameter values reported in the paper takes ~10 hours on a powerful desktop (with no parallelization), or 2- go to https://ucsb.box.com/s/367tvkgnzby61x9nrh64q81748ugaw63 and download the data file "Cavity_data_4EDMD_0" (~3GB) which is the data used in the paper. Using the data file, the program takes about 5 minutes to run on my laptop.
### before you run the code:
go to "./thehood/" and unzip "qpOASES-3.1.0",
then go to subfolder ".\thehood\qpOASES-3.1.0\interfaces\matlab" and run make.m .
This is required to activate the qpOASIS interface for solving the optimization problem.
send comments and questions to
#### arbabiha@gmail.com
H Arbabi
April 2018
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一种基于Koopman模型预测控制(MPC)的非线性流控制的数据驱动框架。内容概要包括Koopman算子的介绍、数据驱动控制框架的构建、非线性流控制的应用实例。适用人群为流体力学、控制理论以及数据科学领域的研究人员和工程师。使用场景涵盖航空航天、气象预报、环境工程等需要精确控制流体动力学的场合。目标是利用数据驱动的方法,提高非线性流体系统的控制精度和效率。 关键词标签: Koopman MPC 数据驱动 非线性流控制
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KoopmanMPC_for_flowcontrol.rar (29个子文件)
KoopmanMPC_for_flowcontrol
thehood
BurgerSolver.m 2KB
CavitySensorLocations.mat 818B
CreateOperators_psi.m 320B
CollectData.m 1KB
getCostMatrix.m 1KB
clencurt.m 502B
CollocationGrid_q.m 838B
PlotVorticity.m 2KB
SystemID_via_EDMD.m 2KB
createMPCmatrices.m 975B
NonlinearFlowSolver.m 4KB
CavityGridOperators.m 2KB
bdiag.m 206B
BigPic.png 106KB
CreateLidVelocity.m 356B
GenerateCavityData.m 2KB
DelayEmbed.m 344B
qpOASES-3.1.0.rar 1.24MB
CavityStateLibrary.mat 927KB
CavitySystemID.m 4KB
cheb.m 371B
RHS_cavity_controlled.m 1KB
qpOases_MPC_controller.m 6KB
CavityExample.m 5KB
LICENSE 1KB
a.txt 28B
BurgersExample.m 6KB
A data-driven Koopman model predictive__control framework for nonlinear flows.pdf 5.81MB
README.md 2KB
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