From 6982ad85199f70766a28e758c16b77369544e07a Mon Sep 17 00:00:00 2001
From: Girard Antoine <antoine.girard@centralesupelec.fr>
Date: Mon, 22 Jan 2024 16:46:04 +0000
Subject: [PATCH] Upload New File
---
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1 file changed, 99 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
+
+% Synthesis of a controller for the specification defined in specification.m
+
+clear
+
+load('symb_abs.mat');
+
+specification;
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Symbolic controller synthesis
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+tic
+
+disp('Step 2: Symbolic controller synthesis')
+
+% Labeling the states
+Lab_xi=zeros(1,n_sigma);
+for xi=1:n_xi
+ c_xi=state2coord(xi,p_x);
+ x_c=bound_x(:,1)+(c_xi-0.5).*d_x; % Coordinates of the center of the cell
+ Lab_xi(xi)=Lab_x(x_c);
+end
+
+% Choice of a sucessor sample
+g_p=zeros(n_s,n_xi,n_sigma);
+for psi=1:n_s
+ g_p(psi,:,:)=g(:,:,1);
+end
+
+%Initialize the value function
+V=inf*ones(n_s,n_xi);
+V(F_s,:)=0; % final states
+
+%Initialize the controller
+h1=@(psi,xi) A_s(psi,Lab_xi(xi));
+h2=zeros(n_s,n_xi);
+
+iter=0;
+fixpoint=0;
+
+while ~fixpoint
+ iter=iter+1;
+ fprintf('Fixed point algorithm: iteration %d \n',iter);
+ Vp=V;
+
+ for xi=1:n_xi
+ for psi=1:n_s
+ psi_succ=h1(psi,xi);
+ if V(psi,xi)==inf
+ if h2(psi_succ,xi)~=0
+ V(psi,xi)=iter;
+ else
+ Vmax=zeros(1,n_sigma);
+ for sigma=1:n_sigma
+ xi_succ=g(xi,sigma,:);
+ if all(xi_succ) % the input is enabled
+ if (Vp(psi_succ,g_p(psi,xi,sigma))~=inf) % the successor sample is controllable
+ c_min=state2coord(xi_succ(1),p_x);
+ c_max=state2coord(xi_succ(2),p_x);
+ if c_min(3)<=c_max(3)
+ Q_succ=coordbox2state(c_min,c_max,grid_xi)' ;
+ else
+ %Special treatment of the third coordinate (angle)
+ %not needed in general
+ Q_succ=[coordbox2state(c_min,[c_max(1);c_max(2);n_x(3)],grid_xi)',...
+ coordbox2state([c_min(1);c_min(2);1],c_max,grid_xi)'];
+ end
+ V_succ=Vp(psi_succ,Q_succ); % list of all successors
+ Vmax(sigma)=all(V_succ~=inf); % check if all successors are controllable
+ if Vmax(sigma)
+ break;
+ else
+ [m,i_p]=max(V_succ~=inf);
+ g_p(psi,xi,sigma)=Q_succ(i_p);
+ end
+ end
+ end
+ end
+ if any(Vmax)
+ % controllable if there exists an input such that all sucessors are controllable
+ V(psi,xi)=iter;
+ [m,sigma]=max(Vmax);
+ h2(psi_succ,xi)=sigma;
+ end
+ end
+ end
+ end
+ end
+ fixpoint=isequal(Vp,V);
+end
+disp('Fixed point reached')
+
+toc
+
+save('symb_synth.mat');
\ No newline at end of file
--
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