% control design for p(y(t+1)|y(t),u(t+1))

function c=condes(sita,IS,IC,my,H)

dis=1;
fil=1;
m=3;
    gamma=ones(1,my);
    alpha=zeros(my,my);

  % computing alpha
   for j=1:my                        % j=u(t+1)  
    for i=1:my                       % i=y(t)
      k=i+my*(j-1);                  % k=y(t) & u(t+1) 
      for i0=1:my                    % i0=y(t+1)
         i1=i0+my*(dis-1)+my*(fil-1)*(m-2);
         alpha(j,i)=alpha(j,i)+sita(i1,k)*log(sita(i1,k)/IS(i0,k));
      end
    end
   end
   
  % computing beta and gamma
  
for t=H-1:-1:1
    % computing beta
    beta=zeros(my,my);
    for j=1:my                   % j=u(t+1)
      for i=1:my                 % i=y(t)
        k=i+my*(j-1);            % k=y(t)&u(t+1)
        for i0=1:my              % i0=y(t+1)
          i1=i0+my*(dis-1)+my*(fil-1)*(m-2);
          beta(j,i)=beta(j,i)-sita(i1,k)*log(gamma(i0));
        end
      end
    end
    
    % computing gamma
    gamma=zeros(1,my);
    for i=1:my            % i=y(t)
      for j=1:my          % j=u(t+1)
        gamma(i)=gamma(i)+IC(j,i)*exp(-alpha(j,i)-beta(j,i));
      end
    end
end

% optimal controller

for j=1:my                    % j=u(t+1)
  for i=1:my                  % i=y(t)
    c(j,i)=(gamma(i))^(-1)*IC(j,i)*exp(-alpha(j,i)-beta(j,i));
  end
end