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symb_sim.m

+, %% Tutorial example on symbolic control
+%% Author: Antoine GIRARD, Universit Paris-Saclay, CNRS, CentraleSuplec, Laboratoire des signaux et systmes, 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')
+