Data-Driven Set-Theoretic Model Predictive Control

This repository contains the codes for "Data-Driven Robust Backward Reachable Sets for Set-Theoretic Model Predictive Control" by Mehran Attar and Walter Lucia jointly has been accepted to publish in IEEE Control Systems Letters (L-CSS) and IEEE Conference on Decision and Control (CDC) --> IEEE link

Problem Statement

Given the input-state trajectories $\mathcal{D}=(x,u)$ collected for the linear model $x_{k+1} = Ax_k + Bu_k + w_k$ with $x_k \in \mathcal{X} \subset \mathbb{R}^n$ and $u_k \in \mathcal{U}\subset \mathbb{R}^m$ and $w_k \in \mathcal{W} \subset \mathbb{R}^n$, with unknown system matrices $(A,B):$

1. Design a data-driven algorithm computing an inner approximation of the ROSC sets $\mathcal{T}^{j} = \lbrace x \in \mathcal{X}: \exists u \in \mathcal{U}: x^+ \in \mathcal{T}^{j-1}, \forall w \in \mathcal{W} \rbrace$

2. Design a Data-Driven Set-Theoretic MPC (D-ST-MPC) controller for the linear system enjoying the same properties of ST-MPC.

Running

1- Download CORA release 2022 and MPT3 release 2022

2- Add CORA and MPT folder and subfolders to the Matlab (in this work, MATLAB R2021-a has been used) path.

3- Add the repo folder and subfolders to the Matlab path.

Files Description

1- To compute ROSC sets based on all consistent system matrices $\hat{A}_i, \hat{B}_i$, run "compute_ROSC_sets.m"

2- To compute ST-MPC control commands and obtain set index membership, run "compute_ST_MPC.m".

Function Descriptions

• "compute_AB.m": computes all possible system matrices that are consistent with the data
• "computeRPI.m": computes a model-based RCI set based on the proposed method in **"Invariant approximations of the minimal robust positively invariant set", by Rakovic et al.
• "model_based_stmpc.m": computes the model-based ST-MPC control commands
• "compute_intersec.m": computes the intersection of polyhedrons
• "compute_presets_approx.m": computes the data-driven ROSC sets in the extended space of $(x,u)$.
• "indx_finder.m": computes the set memebership index of an state for the model-based ROSC sets.
• "one_step_ctrl.m" computes the data-driven ST-MPC control commands.
• "poly_approx.m": computes a zonotopic inner approximation of a polyhedron
• "set_index.m": computes the set memebership index of an state for the data-driven ROSC sets.

Demo

Run "animated_test.m"

Videos

Youtube link