📜 You can find a poster about the toolbox below:
A. Retzler, J. Swevers, J. Gillis, and Zs. Kollár, "Nlgreyfast: toolbox for nonlinear grey-box identification", Flanders Make Conference, Gent, Belgium, 2022.
📽 For a detailed introduction, watch the talks about this project here:
Talk at the 6th Workshop on Nonlinear System Identification Benchmarks:
A shorter talk at the IEEE 17th International Conference on Advanced Motion Control:
🖼 We also have visual documentation that e.g. shows some relations between the formulas and the code, open this large poster, and 🔍 zoom into it with Ctrl+mouse wheel:
This toolbox supports estimating the parameters theta of nonlinear state-space models in the form:
x[k+1]=f(x[k],u[k],theta)
y[k]=g(x[k],u[k],theta)
Such models can often be derived based on physical knowledge of the system. If we have continuous-time ODEs describing the system, we can get a discrete-time model using integration (RK4) from the continuous-time model.
The parameter estimation task is ultimately about solving an optimization problem, of which this toolbox supports multiple formulations (these can also be regarded as a form of optimal control):
- single shooting (SS),
- multiple shooting (MS),
- partially constrained multiple shooting (PCMS),
- minimizing the N-step ahead prediction error (PEM).
The objective is always to minimize the least squares error between the noisy, measured system output and the simulated one, and is almost always non-convex, so the initial guess of the parameters play an improtant role. The MS, PCMS and especially the PEM formulations are more robust against initial values of the decision variables in a range where the system becomes unstable, in other words the simulation of the states becomes non-contractive.
Moreover, if the states can be measured or inferred, this toolbox can use this information in the estimation (it is required for PEM, but it can also be used in PCMS/MS for initializing the decision variables). In our experiments on a simple, simulated electromechanical system (see EMPS later), we have found that if we have the measured and inferred states, the combined PEM+SS method is the most robust against a non-contractive initialization point, and it is also the best choice with respect to running time.
For optimization this tool uses CasADi, so that it can solve certain problems a magnitude faster than nlgreyest that ships with the System Identification Toolbox of MATLAB. This can be interesting for applications of online identificiation, e.g. identification combined with control.
You can find more details about these in our paper.
The basic steps of identification using this toolbox:
- Design, build an perform experiment for system identification. Measure plant input and output.
- Define the grey-box model of your system in CasADi, as a continuous or discrete time nonlinear state-space model.
- Choose formulation for the optimization problem, use
nlgreyfastto estimate the model parameters.
All right, how to install it?
First, install the dependencies:
- MATLAB (tested with R2019b on Ubuntu),
- CasADi (tested with version 3.5.5), available here.
- Optional: MathWorks System Identification Toolbox (if not available, you can still use the
nlidcombinterface). - Optional: MATLAB Coder
Second, go through the script nlgreyfast_emps_example.m step by step.
For an example of the nlidcomb interface, see: nlidcomb_msd_example.m.
Authors of the code in this package:
- András Retzler
- Joris Gillis --
nlgreyfastis based on Joris' CasADi implementation of the MS and SS method.
This research is supported by Flanders Make through ICON project ID2CON: Integrated IDentification for CONtrol, and by the Research Foundation - Flanders (FWO - Flanders) through project G0A6917N.
Special thanks to Alexandre Janot, Mathieu Brunot, Maxime Gautier for their EMPS model and measurement data:
A. Janot, M. Gautier and M. Brunot, "Data Set and Reference Models of EMPS", 2019 Workshop on Nonlinear System Identification Benchmarks, Eindhoven, The Netherlands, April 10-12, 2019.
The source of data in nlid_emps_sim_data_training.mat and part of the code related to EMPS is the package available here.
If you use this toolbox in your research, please cite:
A. Retzler, J. Swevers, J. Gillis, and Zs. Kollár, "Shooting methods for identification of nonlinear state-space grey-box models", IEEE 17th International Conference on Advanced Motion Control, Padova, Italy, 2022.