From 7be1a0c669942dda84a804a43428112c12c26e47 Mon Sep 17 00:00:00 2001
From: Girard Antoine <antoine.girard@centralesupelec.fr>
Date: Mon, 22 Jan 2024 16:45:25 +0000
Subject: [PATCH] Upload New File
---
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1 file changed, 63 insertions(+)
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+, %% Tutorial example on symbolic control
+%% Author: Antoine GIRARD, Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des signaux et systèmes, 91190, Gif-sur-Yvette, France.
+%% Date: 2024
+
+% Simulation of closed-loop trajectories
+
+clear
+
+load('symb_synth.mat');
+
+figure(3)
+hold on
+fill([R1(1,1) R1(1,2) R1(1,2) R1(1,1)],...
+ [R1(2,1) R1(2,1) R1(2,2) R1(2,2)],'y','FaceAlpha',0.4);
+fill([R2(1,1) R2(1,2) R2(1,2) R2(1,1)],...
+ [R2(2,1) R2(2,1) R2(2,2) R2(2,2)],'c','FaceAlpha',0.4);
+fill([R3(1,1) R3(1,2) R3(1,2) R3(1,1)],...
+ [R3(2,1) R3(2,1) R3(2,2) R3(2,2)],'g','FaceAlpha',0.4);
+fill([R4(1,1) R4(1,2) R4(1,2) R4(1,1)],...
+ [R4(2,1) R4(2,1) R4(2,2) R4(2,2)],'r','FaceAlpha',0.4);
+
+
+num_step=100;
+
+x0=ones(3,50).*[6.8;9;0];
+%x0=[[0.5;4.5;0],[0.5;4;0]];
+
+for i=1:size(x0,2)
+
+x=x0(:,i);
+psi=I_s;
+z=x;
+Tx=[x];
+for t=1:num_step
+
+ psi=h1(psi,q(x));
+
+
+ if psi==F_s
+ break;
+ end
+ u=p(h2(psi,q(x)));
+ w=bound_w(:,1)+diag(rand(3,1))*d_w;
+ x=f(x,u,w);
+ z=f(z,u,w);
+ if x(3)>pi
+ x(3)=x(3)-2*pi;
+ elseif x(3)<-pi
+ x(3)=x(3)+2*pi;
+ end
+ Tx=[Tx,z];
+end
+plot(Tx(1,:),Tx(2,:),'-o','color','r');
+%plot(Tx(1,:),Tx(2,:),'-o');
+end
+hold off
+axis([bound_x(1,1) bound_x(1,2) bound_x(2,1) bound_x(2,2)]);
+ax = gca;
+ax.FontSize = 16;
+xlabel('x_1');
+ylabel('x_2');
+title('Trajectories of the closed-loop system')
+
--
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