Optimal Instrumental Variable Selection for Closed-loop Data-Driven Predictive Control

This repository provides the code code that was employed to arrive at the results presented in Optimal Instrumental Variable Selection for Closed-loop Data-Driven Predictive Control by
Rogier Dinkla¹, Tom Oomen^1,2, Sebastiaan P. Mulders¹, and Jan-Willem van Wingerden¹.

Affiliations:
¹ Delft Center for Systems and Control, Faculty of Mechanical Engineering, Delft University of Technology, The Netherlands
² Control Systems Technology Group, Department of Mechanical Engineering, Eindhoven University of Technology, The Netherlands

Prerequisites

Required Software:

• MATLAB R2024b (or compatible) with toolboxes:

  Toolbox	Version
  Control System Toolbox	v24.2
  Robust Control Toolbox	v24.2
  Statistics and Machine Learning Toolbox	v24.2
  System Identification Toolbox	v24.2
  Parallel Computing Toolbox	v24.2

  • Check installation: Run ver in MATLAB to verify toolbox availability
  • License: Proprietary (academic license used; see MathWorks licensing options)

• CasADi v3.6.7

  • License: LGPL v3.0 (open source)
  • Purpose: Symbolic differentiation. Used for symbolic computations to obtain a SPC-type controller (see src/MC_sim/get_solver.m).

• Crameri colormaps v7.0+ (required for paper figures)

  • License: MIT (open source, see MATLAB file exchange -> Zenodo)
  • Purpose: Perceptually uniform scientific colormaps (linear colour gradients among other features).

High-Performance Computing (optional):

• Data was generated and processed using the DelftBlue supercomputer. Use of a comparable high-performance computer (HPC) is optional. Code is tailored to the potential use of an HPC with SLURM scheduling.

This Code Repository

• License: MIT License (see LICENSE.md)
• Copyright: (c) 2026 Data-Driven Control, TU Delft

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Installation

Automated installation using INIT.m:

• Edit SLURM cluster configuration settings in INIT.m before running (optional — only needed if using a SLURM cluster)
• Run the INIT.m file from the project directory. The output should resemble (using Windows here)

================= CasADi v3.6.7 ==================
  -------------- SYSTEM DETECTION ---------------
  MATLAB release : 2024b
  Platform       : windows

  ------------ SELECTING DEPENDENCIES -----------
  CasADi: Selected Windows 64-bit binary

  ----------- INSTALLING DEPENDENCIES -----------
  >> Downloading from GitHub...         Done
  >> Extracting files...                Done
  >> Verifying installation...          Done

============== Crameri colour maps ===============
  >> Downloading from GitHub...         Done
  >> Extracting files...                Done
  >> Verifying installation...          Done

Manual installation:

Step 1: Add the src directory to the path

From the project directory in MATLAB, run:

addpath(genpath('src'));

Step 2: SLURM Configuration (optional)

Specify the following parameters in MATLAB and save them to src/SlurmSettings.mat:

ProfileName = ''; % Enter profile name used for the SLURM cluster (e.g., 'MyClusterProfile')
account     = ''; % Enter account e.g. 'institution-department'
partition   = ''; % Enter partitions to use, comma-separated if multiple (e.g., 'partition1,partition2')
save(fullfile('src','SlurmSettings.mat'),'account','partition','ProfileName');

N.B.: The above parameters may be left empty if no SLURM cluster is used, but the file must be saved as shown.

Step 3: Download CasADi

The code project uses CasADi v3.6.7:

1. Download CasADi from casadi.org (version 3.6.7)
2. Extract the contents to: bin/casadi-v3.6.7/
3. Add the directory to the path:

   addpath(fullfile('bin','casadi-v3.6.7'));

4. Verify CasADi was installed properly by running:

   x = casadi.SX.sym('x');
   fprintf('CasADi loaded successfully.\n');

Step 4: Install Crameri Colormaps

1. Download Crameri colormaps
2. Extract the contents to: bin/crameri_colours/
3. Add to path:

   addpath(fullfile('bin','crameri_colours'));

4. Verify installation by running the below command (should open an illustration of available colormaps).

   crameri

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Running the code

Reproducing results from the article

Option A: Run Simulations -> Process Data -> Visualize results

• step 1) Run main_dRe()
  • This generates a batch of Monte Carlo simulations for varying Re (innovation noise variance).
  • The parent directory for all of this data should be of the form
    data/sys1/ref0_prbs/dRe/Re_1e-05_1e-01_15_p_20_N_1e03_f_20_YYYYMMDD_HHmm/
• step 2) Run main_processing
  • This produces a processed_data.mat file in the parent directory mentioned directly above.
• step 3) Edit the timestamp of the repository referenced by the subdir1 variable in plot_figs_paper.m.
• step 4) Run plot_figs_paper
  • This will produce all of the plots from the paper.

Option B: Download (Processed) Data -> Visualize results

• step 1) Download raw & processed data from Zenodo:
• step 2) Create the folder data/sys1/ref0_prbs/dRe/Re_1e-05_1e-01_15_p_20_N_1e03_f_20_20260327_1942 and extract the contents of the zipfile thereto.
• step 3) Run plot_figs_paper

Generating other results

Important parameters that the user can change for different data sets are

Parameter	Default	Description
Re	0.01	Innovation noise variance
N	1000	Number of columns in Hankel data matrix
p	20	Past horizon (learning window length)
f	20	Future horizon (prediction/control window)
Ncl	1500	Closed-loop simulation length
seed	1	Random seed for reproducibility
sys	1	System configuration (1 = Landau1995, primary)
ref0	'prbs'	Initial reference signal type: 'make*' or 'prbs'
Qk, Rk, dRk	100, 1, 1	Controller cost weights

*'make' specifies an initial reference that is based on the reference used in [25]. The output reference trajectory that is employed by the different controllers is always based on such a reference and not a 'prbs' variant.

A single Monte Carlo simulation can be run using the main function. Alternatively, batches of Monte Carlo simulations that perform a parameter sweep are performed by the functions

• main_dRe - Parameter sweep over Re (innovation noise variance).
• main_dp - Parameter sweep over p (past window length).
• main_dN - Parameter sweep over N (number of Hankel matrix columns).

Each of the main_d<X> functions by default performs 100 Monte Carlo simulations per value of Re, p, or N.

For execution on a SLURM cluster:

1. Configure SLURM settings via src/SlurmSettings.mat (see installation section above)
2. Running main_dRe, main_dp, or main_dN will automatically:
   • Detect SLURM settings from SlurmSettings.mat
   • Submit and manage job runtime via run_X_ParCluster.m
   • Save results to an appropriately named data directory

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References

[25] A. Chiuso, M. Fabris, V. Breschi, and S. Formentin, "Harnessing uncertainty for a separation principle in direct data-driven predictive control," Automatica, vol. 173, p. 112070, Mar. 2025, doi: 10.1016/j.automatica.2024.112070.