Code for paper "Joint state and dynamics estimation with high-gain observers and Gaussian process models", by Mona Buisson-Fenet, Valéry Morgenthaler, Sebastian Trimpe, and Florent Di Meglio. Focusing on a dynamical system in observable canonical form with an unknown nonlinearity, the aim is to jointly estimate the state with a high-gain observer and the nonlinearity with a Gaussian process model.

To reproduce the results from the paper:

• create a directory for this repo, further named dir
• create dir/Figures/Logs
• clone this repo in dir/repo
• create a python3 virtual environment for this repo in dir/venv, source it
• install all requirements with pip (pip install -r repo/requirements.txt)
• if any problems occur during the installation of required packages, see requirements.txt for possible fixes
• if you want to use multivariate Gaussian priors for hyperparameter optimization, replace the file priors.py in your virtual environment dir/venv/lib/python3.7/site-packages/GPy/core/parametrization/ by the file dir/repo/priors.py (pull request pending)
• cd repo, run python mass_spring_mass_testcase/MSM_observer_GP.py 1 (1 = process number, used for logging)

This will run the simulation described in the paper for 10 cycles from 10 random initial conditions, with 10 test trajectories used for evaluation at each cycle. Modify the config parameters in the script to change the settings.

To play with other methods and test cases, look into the quasilinear_observer_GP.py file and choose which system and method to use, then run python quasilinear_observer_GP.py 1

To cite this paper:

@article{LCSSpaper,  
author={M. {Buisson-Fenet} and V. {Morgenthaler} and S. {Trimpe} and F. {Di Meglio}},  
journal={IEEE Control Systems Letters},   
title={Joint State and Dynamics Estimation With High-Gain Observers and Gaussian Process Models},   
year={2021},  
volume={5},  
number={5},  
pages={1627-1632},  
doi={10.1109/LCSYS.2020.3042412}
}