This repository contains code for the article
@inproceedings{gao2024learning,
title={Learning-based Rigid Tube Model Predictive Control},
author={Yulong Gao, Shuhao Yan, Jian Zhou, Mark Cannon, Alessandro Abate, and Karl H. Johansson},
booktitle={Learning for Dynamics and Control Conference},
year={2023},
pages={}
} which has been accepted for presentation and publication at the 6th Annual Learning for Dynamics & Control Conference (L4DC), 2024.
To run the code you need to install:
CasADi: https://web.casadi.org/;
MPT: https://www.mpt3.org/Main/Installation; (The installation will automatically install Yalmip, which is also necessary for running the code.)
Calculate and define all parameters and save the results in parameters.mat. Since the parameters have been provided in the repository, if you do not want to update those values you can avoid running this file.
Compute the minimum robust positive invariant set $\mathbb{S}$.
Compute the feasible region corresponding to different disturbance sets, e.g., $\mathbb{W}$, $\mathbb{W}_{\rm true}$, and $\hat{\mathbb{W}}_k^{\star}$.
Learn the initial uncertainty set $\hat{\mathbb{W}}^{\star}_0$ based on $\mathbb{W}$, using initial information set $\mathcal{I}_0^w$.
Modeling of the ego vehicle (EV) and the leading vehicle (LV).
Conventional Robust MPC controller.
The proposed uncertainty quantification-based Robust MPC controller.
The scenario MPC controller.
Compute the feasible region of UQ-RMPC and nominal RMPC, results are saved in Results/Results_1.mat, and figures are produced by Results/Fig_Case_1.m.
Monte-Carlo simulation learning the set $\mathbb{W}_{\rm true}$ with different sizes of initial information set $\mathcal{I}_0^w$, results are saved in Results/Results_2.mat, and figures are produced by Results/Fig_Case_2.m.
Online evaluation of UQ-RMPC with different initial information set $\mathcal{I}_0^w$, results are saved in Results/Results_3_large.mat ($|\mathcal{I}_0^w| = 20000$) and Results/Results_3_small.mat ($|\mathcal{I}_0^w| = 100$), and figures are produced by Results/Fig_Case_3.m.
Monte-Carlo simulation of UQ-RMPC when the simulation time is long enough, results are saved in Results/Results_4.mat, and figures are produced by Results/Fig_Case_4.m.
Monte-Carlo simulation to evaluate the feasibility of UQ-RMPC with different initial information set $\mathcal{I}_0^w$, 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.
Comparing the computation time with Scenario MPC.
(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 $\nu_k$ 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 $\nu_k$. In practical applications, we can make $\nu_k$ long enough such that the condition on $\nu_k$ will be satisfied. For example, a suggestion can be $\nu_k = 2\nu_s$.