Upload New File

Demos for MATLAB/Example4_hom_unit_control/demo_ANN_hom_unit_control.m

+%%% hANN for homogeneous unit control and simulations  
+
+A=[0 3 0 0 0;
+   -3 0 0 0 0;
+   0 0 1 -1 1;
+   0 1 0 2 1;
+   1 0 1 -1 3];  %  system matrix
+
+B=[0 0;
+   0 0;
+   0 0;
+   1 0;
+   0 1]; % control matrix
+
+C=[0 0 1 0 0;
+   0 0 0 1 0;
+   0 0 0 0 1]; % sliding surface  Cx=0
+
+n=5;m=2; p=3;
+rho=1; %convergence rate tuning parameter (learger rho faster the convergence) 
+gamma_max=0.5; % 0.4 - magnitude of perturbation + 0.1 gap for approximation error 
+
+[K0 K Gd P]=hsmc_design(A,B,C,rho,gamma_max); %design the parameteres of hom. unit SMC 
+
+%K0 - homogenization gain
+%K  - control gain
+%Gd - generator of dilation
+%P  - shape matrix of the weighted Euclidean norm
+
+
+
+%%%% definition of an explicit hom norm %%%
+
+
+rb=1;                                                                      
+[Q L J]=approx_hnorm_weight(Gd,P,rb,30);            %param. of explicit hom. norm
+
+hn_fun=@(x)hnorm_weight(x,L,rb,Q,J);               %explicit hom. norm
+
+
+%%%% Approximation of hom. proj by hANN %%%
+
+[xi Theta W]=approx_hproj_sigmoid(Gd,P,hn_fun,10);
+
+
+%%%%%%  check an approximation error
+%x=[1;2;3];
+%hann(x,Theta,xi,W,Gd,0,hn_fun)
+%hproj(x,Gd,P)
+%return
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+t=0; Tmax=4; 
+h=0.001; % sampling period
+
+x=[1;0;2;0;1];
+tl=[t];xl=[x];ul=[];
+
+
+
+noise=0.00;    % magnitude of measurement noises 
+
+disp('Run numerical simulation...');
+
+[Ah, Bh]=ZOH(h,A,B);
+tic
+while t<Tmax
+    xm=x+2*noise*(rand(5,1)-0.5);                  %(possibly) noised state
+
+    %u=(K0+K*C)*xm;                       % linear control (for comparison)
+      
+    u=K0*xm+K*hann(C*xm,Theta,xi,W,Gd,0,hn_fun);       % explicit discretization of HSMC
+    
+    %u=si_hsmc(h,xm,A,B,C,K0,K,Gd,P,alpha); %semi-implicit discret. of HSMC
+    
+    gamma_t=(gamma_max-0.1)*[sin(2*t);cos(10*t)];          % matched perturbation 
+
+    x=Ah*x+Bh*(u+gamma_t);                        %simulation of the system
+
+    t=t+h;
+    tl=[tl t];
+    xl=[xl x];
+    ul=[ul u];
+end;
+toc
+ul=[ul u];
+
+disp('Done!');
+
+%%%%%%%%%%%%%%%%%%%%%%%%%
+% Plot simulation results
+%%%%%%%%%%%%%%%%%%%%%%%%%
+figure;
+axes1 = subplot(1,2,1);
+hold(axes1,'on');
+plot1 = plot(tl,xl,'LineWidth',2,'Parent',axes1);
+set(plot1(1),'DisplayName','$x_1$');
+set(plot1(2),'DisplayName','$x_2$');
+set(plot1(3),'DisplayName','$x_3$');
+set(plot1(4),'DisplayName','$x_4$');
+set(plot1(5),'DisplayName','$x_5$');
+ylabel('$x$','Interpreter','latex');
+xlabel('$t$','Interpreter','latex');
+title({'n=5'});
+xlim(axes1,[0 Tmax]);
+ylim(axes1,[-3 3]);
+box(axes1,'on');
+hold(axes1,'off');
+set(axes1,'FontSize',30,'XGrid','on','YGrid','on');
+legend1 = legend(axes1,'show');
+set(legend1,'Interpreter','latex');
+
+
+axes2 = subplot(1,2,2);
+hold(axes2,'on');
+plot2 = plot(tl,ul,'LineWidth',2);
+set(plot2(1),'DisplayName','$u_1$');
+set(plot2(2),'DisplayName','$u_2$');
+ylabel('$u$','Interpreter','latex');
+xlabel('$t$','Interpreter','latex');
+title({'HSMC,m=2'});
+xlim(axes2,[0 Tmax]);
+ylim(axes2,[-12 12]);
+box(axes2,'on');
+hold(axes2,'off');
+set(axes2,'FontSize',30,'XGrid','on','YGrid','on');
+legend2 = legend(axes2,'show');
+set(legend2, 'Interpreter','latex');
+
+
+
+
+
+