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:

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.

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.

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

H Arbabi

April 2018