last commit

All_AB.m

@@ -0,0 +1,105 @@
+% Author:       Mehran Attar
+% Written:      08-March-2023
+% Last update:
+% Last revision:---
+
+%------------- BEGIN CODE --------------
+clc
+clear all
+close all
+%% system dynamics
+A=[0.7969 -0.2247;
+    0.1798 0.9767];
+B=[0.1271;0.0132];
+C = [1,0];
+D = 0;
+rand('seed',1);
+% define continuous time system
+% sys_c = ss(A,B,C,D);
+% % convert to discrete system
+% samplingtime = 0.01;
+% sys_d = c2d(sys_c,samplingtime);
+dim_x = size(A, 2);
+initpoints =1;
+%Number of time steps
+steps = 4;
+totalsamples = initpoints*steps;
+%% initial set and input
+% X0 = zonotope(zeros(dim_x,1),diag(ones(dim_x,1)));
+% X0 = zonotope(zeros(2,1),0.106*[0.999 -0.1;-1 -1]);
+U = zonotope(0,3);
+X0 = zonotope(zeros(2,1),10*eye(2));
+%noise zontope W
+W = zonotope(zeros(dim_x,1),0.005*eye(dim_x));
+
+%Construct matrix zonotpe \mathcal{M}_w
+index=1;
+for i=1:size(W.generators,2)
+    vec = W.Z(:,i+1);
+    GW{index}= [vec,zeros(dim_x,totalsamples-1)];
+    for j=1:totalsamples-1
+        GW{j+index}=  [GW{index+j-1}(:,2:end) GW{index+j-1}(:,1)];
+    end
+    index = j+index+1;
+end
+Wmatzono= matZonotope(zeros(dim_x,totalsamples),GW);
+
+% randomly choose constant inputs for each step / sampling time
+for i=1:totalsamples
+    u(i) = randPoint(U);
+end
+
+%simulate the system to get the data
+x0 = X0.center;
+x(:,1) = x0;
+index=1;
+for j=1:dim_x:initpoints*dim_x
+    x(j:j+dim_x-1,1) = randPoint(X0);
+    for i=1:steps
+        utraj(j,i) = u(index);
+        x(j:j+dim_x-1,i+1) = A*x(j:j+dim_x-1,i) + B*u(index) + randPoint(W);
+        index=index+1;
+    end
+end
+
+% concatenate the data trajectories
+index_0 =1;
+index_1 =1;
+for j=1:dim_x:initpoints*dim_x
+    for i=2:steps+1
+        x_meas_vec_1(:,index_1) = x(j:j+dim_x-1,i);
+        index_1 = index_1 +1;
+    end
+    for i=1:steps
+        u_mean_vec_0(:,index_0) = utraj(j,i);
+        x_meas_vec_0(:,index_0) = x(j:j+dim_x-1,i);
+        index_0 = index_0 +1;
+    end
+end
+
+% X_+ is X_1T
+% X_- is X_0T
+U_full = u_mean_vec_0(:,1:totalsamples); %same as u
+X_0T = x_meas_vec_0(:,1:totalsamples);
+X_1T = x_meas_vec_1(:,1:totalsamples);
+
+X1W_cen =  X_1T - Wmatzono.center;
+X1W = matZonotope(X1W_cen,Wmatzono.generator);
+% set of A and B
+AB = X1W * pinv([X_0T;U_full]);
+
+%%
+
+matrixCenter = [AB.center;zeros(1,3)];
+
+for i=1:AB.gens
+  G{i}=[AB.generator{i};zeros(1,3)];  
+end
+
+% instantiate matrix zonotope
+M_zono = matZonotope(matrixCenter, G);
+
+% obtain result of all vertices-------------------------
+V_AB = vertices(M_zono);
+
+save V_AB

README.md

@@ -1,20 +1,19 @@
 # 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](https://scholar.google.com/citations?user=nnLTy-oAAAAJ&hl=en) and [Walter Lucia](https://users.encs.concordia.ca/~wlucia/index.html), jointly submitted to IEEE Control Systems Letters (L-CSS) and IEEE Conference on Decision and Control (CDC) 
-[arXiv pre-print link](https://arxiv.org/abs/2303.04749)
+This repository contains the codes for "Data-Driven Robust Backward Reachable Sets for Set-Theoretic Model Predictive Control" by [Mehran Attar](https://scholar.google.com/citations?user=nnLTy-oAAAAJ&hl=en) and [Walter Lucia](https://users.encs.concordia.ca/~wlucia/index.html) jointly has been accepted to publish in IEEE Control Systems Letters (L-CSS) and IEEE Conference on Decision and Control (CDC) --> [IEEE link](https://ieeexplore.ieee.org/abstract/document/10153604)
+
 
 ### 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 $\mathcal{T}^{j} = {x \in \mathcal{X}: \exists u \in \mathcal{U}: x^+ \in \mathcal{T}^{j-1}, \forall w \in \mathcal{W} \}$
+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. 
+2. Design a Data-Driven Set-Theoretic MPC (D-ST-MPC) controller for the linear system enjoying the same properties of [ST-MPC](https://www.sciencedirect.com/science/article/pii/S0005109808003014?casa_token=n_C40ZvVjWEAAAAA:y8PyF290r0VL7DdULvbDI1oRdR9I1yO__-ag8JSzWvxPO3AFZTa10AtTl6NMu552nhrUk4ZV). 
 
 ## Running
 1- Download [CORA release 2022](https://tumcps.github.io/CORA/) and [MPT3 release 2022](https://www.mpt3.org/) 
 
-2- Add CORA and MPT folder and subfolders to the Matlab (in this work, [MATLAB R2021-a has been used](https://www.mathworks.com/products/new_products/release2021a.html)) path.
+2- Add CORA and MPT folder and subfolders to the Matlab (in this work, [MATLAB R2021-a](https://www.mathworks.com/products/new_products/release2021a.html) has been used) path.
 
 3- Add the repo folder and subfolders to the Matlab path.
 
@@ -25,8 +24,8 @@ Given the input-state trajectories $\mathcal{D}=(x,u)$ collected for the linear
 
 #### 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 Rokovic**
-- "commandcalculation.m": computes the model-based ST-MPC control commands
+- "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. 
@@ -39,6 +38,6 @@ Given the input-state trajectories $\mathcal{D}=(x,u)$ collected for the linear
 Run "animated_test.m"
 
 ## Videos
-Check [PreCyse Research Group Youtube channel](https://www.youtube.com/@precysegroup9944)
+[Youtube link](https://www.youtube.com/watch?v=BQ3rUl_VqJs)