Try this:
t=0;
x=[1,1,1];
v=x(1);
vc=sin(t+1)-cos(0.5*t-2);
sigma=v-vc;
alpha=30;
tau=0.0001;
k = 1; % Counter
while t<=10
f=-sin(t+5)-0.5*cos(t)-x(2);
v=x(1);
vc=sin(t+1)-cos(0.5*t-2);
vcc=cos(t+1)+0.5*sin(0.5*t-2);
sigma=v-vc;
sigmadot=f-vcc;
u=alpha*((abs(sigmadot)).^2*sign(sigmadot)+sigma)/((sigmadot).^2+abs(sigma));
dx=[f,cos(1+x(1)+x(3))+(2-cos(x(1)+x(3)+1))*u,cos(x(1)+0.5*x(3)-t)-x(3)+u];
x=x+dx*tau;
t=t+tau;
sigmav(k) = sigma; % Vector
uv(k) = u; % Vector
tv(k) = t; % Vector
k = k + 1; % Increment Countr
end
figure
plot(tv, uv)
grid
figure
plot(tv, sigmav)
grid
