Data Driven Reachability Analysis from Noisy Data

This repo contains the code for our two papers:

1- Amr Alanwar, Anne Koch, Frank Allgower, Karl Johansson "Data Driven Reachability Analysis using Matrix Zonotopes" 3rd Annual Learning for Dynamics and Control Conference ( link )

2- Amr Alanwar, Anne Koch, Frank Allgower, Karl Johansson "Data Driven Reachability Analysis from Noisy Data" IEEE Transactions on Automatic Control ( link )

L4DC Short video about the idea

Problem Statement

We consider the problem of reachability analysis from noisy data, given that the system model is unknown. Identifying a model is a preliminary step in the state-of-the-art reachability analysis approaches. However, systems are becoming more complex, and data is becoming more readily available. We propose a data-driven reachability analysis using matrix zonotope and using a new set representation named constrained matrix zonotope.
The following figure summarizes the idea behind our papers.

Files Description

There are two levels of complexity for the proposed data driven reachability analysis
A- Basic reachability analysis under the folder examples-basic

B- Advanced reachability analysis using constrained matrix zonotope under the folder examples-cmz. These files compare three methods for reachability analysis namely, matrix zonotope, constrained matrix zonotop using exact noise description and constrained matrix zonotope given side information.

Running

1- Download CORA 2020 and MPT toolboxs.
2- Add CORA and MPT folder and subfolders to the Matlab path.
3- Add the repo folder and subfolders to the Matlab path.

Basix reachablity under the folder examples-basic:

1- run a_linearDT.m for linear system using matrix zonotope.
2- run a_nonlinearDT.m for nonlinear system.
3- run a_polyDT.m for polynomial system using matrix zonotope.

Advanced reachablity under the folder examples-cmz:

1- run b_linearDT_measnoise.m for linear system with measurement noise.
2- run b_linearDT_sideInfo.m for linear system given side information.
3- run b_polyDT_sideInfo.m for polynomial system given side information.


You can save the workspace after any advanced reachability file (folder examples-cmz) and then run the plotting file under the folder plotting.
For example, run
b_linearDT_sideInfo.m
save the workspace and load it later then run
p_plot_linearDT_sideInfo.m





Our papers Bibtex are as follow:

@InProceedings{pmlr-v144-alanwar21a,
  title = 	 {Data-Driven Reachability Analysis Using Matrix Zonotopes},
  author =   {Alanwar, Amr and Koch, Anne and Allg\"ower, Frank and Johansson, Karl Henrik},
  booktitle ={Proceedings of the 3rd Conference on Learning for Dynamics and Control},
  pages = 	 {163--175},
  year = 	 {2021},
  volume = 	 {144},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {07 -- 08 June},
  publisher =    {PMLR},
 }

@ARTICLE{10068731,
  author={Alanwar, Amr and Koch, Anne and Allgöwer, Frank and Johansson, Karl Henrik},
  journal={IEEE Transactions on Automatic Control}, 
  title={Data-Driven Reachability Analysis from Noisy Data}, 
  year={2023},
  volume={},
  number={},
  pages={1-16},
  doi={10.1109/TAC.2023.3257167}}