lee-ck / Tube-Robust-MPC-with-Uncertainty-Quantification

This is the MATLAB code for tube robust MPC with uncertainty quantification

Tube-Robust-MPC-with-Uncertainty-Quantification

This is the MATLAB code for tube robust MPC with uncertainty quantification.

Packages for running the code

To run the code you need to install:

CasADi: https://web.casadi.org/ (please find the version that fits your computer and MATLAB);

MPT: https://www.mpt3.org/Main/Installation (you can choose either Automatic installation or Manual installation; when you have installed MPT you will automatically install YALMIP);

SDPT3-4.0: https://blog.nus.edu.sg/mattohkc/softwares/sdpt3/ (Installation of SDPT3-4.0 and configuration can be a bit comprehensive, you may need a few Mex files. Then you need to open MATLAB in the directory SDPT3-4.0, then in MATLAB command window, type:

Installmex(1)

to activate the SDP solver. But it is not necessary to run the code, this is only needed to compute $P_s$ in line 161 in the file offline_parameters_computation.m. You can avoid running this file and only use the provided parameters, such that you do not need to install the solver.)

The file offline_parameters_computation.m

This is the first file you need to run to get all parameters computed offline, it may take some time, and the results will be automatically saved in parameters.mat. The parameters have been provided in the code so if you do not want to update those values you can avoid running this file.

The Functions folder

compute_mrpi_set.m:

A function to compute the RPI set, implemented according to: Rakovic, Sasa V., et al. "Invariant approximations of the minimal robust positively invariant set." IEEE Transactions on automatic control 50.3 (2005): 406-410.

ComputeFeasibleRegion.m

A function to compute the feasible region corresponding to different disturbance sets, e.g., $\mathbb{W}$, $\mathbb{W}_{\rm true}$, and so on.

InitialSetComputation.m

A function to initiate the uncertainty quantification of the set $\mathbb{W}_{\rm true}$ based on $\mathbb{W}$, using initial information set $\mathcal{I}_0^w$.

ModelingCar.m

A function for modeling the EV and LV

NominalRobustMPC.m

A function for the conventional Robust MPC controller

UQRobustMPC.m

A function for the uncertainty quantification Robust MPC controller

The Cases folder

Case_1.m

The file to get Fig. 1, corresponding results are saved in Results/Results_1.mat, and figures are produced by Figures/Fig_Case_1.m.

Case_2.m

The file to get Fig. 2, corresponding results are saved in Results/Results_2.mat, and figures are produced by Figures/Fig_Case_2.m.

Case_3.m

The file to get Fig. 3-4, corresponding results are saved in Results/Results_3_large.mat (i.e., $|\mathcal{I}_0^w| = 20000$) and Results/Results_3_small.mat (i.e., $|\mathcal{I}_0^w| = 100$), and figures are produced by Figures/Fig_Case_3.m.

Case_4.m

The file to get Fig. 5, results are saved in Results/Results_4.mat, and figures are produced by Figures/Fig_Case_4.m.

Case_5.m

The file to get Table I, results are saved in Results/Results_5.mat, e.g., Results_5_10.mat indicates the results with $|\mathcal{I}_0^w| = 10$, and so on.

The Results folder

The folder saves the data by running the files in the folder Cases by the author. If you run the files in the folder Cases, the data will be saved in the main directory then you need to manually move it to the Results folder

The Figures folder

This folder saves the files for making the figures used in the article, you can directly run them to reproduce the figures.

Some implementation details

(1) It is not necessary to run offline_parameters_computation.m if you do not want to update the parameter values, but you need to run run_first.m to add the path of folders.

(2) In the article, the horizon $\nu_k$ in (20) is updated according to Algorithm 1, but this will change the number of constraints of MPC. In our code, we implemented Algorithm 1 and found that $\nu_k$ is almost equal to $\nu_s$. Therefore, we use $\nu_s$ to replace $\nu_k$ (see line 136 in the file offline_parameters_computation.m). In practical applications, we can make $\nu_k$ long enough such that the condition on $\nu_k$ such that the condition above Algorithm 1 will be satisfied. For example, a suggestion can be $\nu_k = 2\nu_s$.