Does MPC with fmincon from a Matlab script work with a Simulink model?

I want to run MPC in Matlab, where I optimize the input U, which is fed into a Simulink model and then calculates the state trajectory of my system. The Simulink model is a trivial, discrete LTI-system. The goal is to have an arbitrary system later.

Here is a screenshot of the given system:

So for this system, I want to minimize the input "input_model" by using fmincon from a matlab script.

The definition of the optimization problem is as follows:

op = optimoptions('fmincon','Algorithm','sqp');
cost_fun = @(u)MPC_cost(u,x_current,Q,R,N,t_start_MPC,t_sample);
opt = fmincon(cost_fun,u0,[],[],[],[],u_min,u_max,[],op);

where u is the input to optimize, x_current is the current system state gained from the Simulink model, Q,R are the weighting matrices for the cost function, N is the prediction horizon, t_start_MPC the starting time (needed for the FromWorkspace block "input_model") and t_sample the fundamental sampling time.

function cost = MPC_cost(U,x_current,Q,R,N,t_start_MPC,t_sample)
%% init state prediction
x_pred = zeros(2,N+1);
u_MPC = zeros(N,2);
x_pred(:,1) = x_current;
%% optimization variable U
u_MPC(:,1) = t_start_MPC:t_sample:(t_start_MPC + (N-1)*t_sample);
u_MPC(:,2) = U;
input_model = u_MPC;
%% simulation to optimize input
x_init = x_pred(:,1);
optimization.StartTime = num2str(t_start_MPC);
optimization.StopTime = num2str((t_start_MPC + (N-1)*t_sample));
x_MPC = sim("Simu.slx",optimization);
%% state prediction vector from simulation 
x_pred = x_MPC.xout.getElement(1).Values.data';
%% init cost
sum = 0;
%% cost function under prediction
for J = 1:N
  sum = sum + x_pred(:,J)'*Q*(x_pred(:,J)) + U(J)'*R*U(J); 
end 
cost = sum;
end

The cost function to optimize is of the form .

As can be seen I first initalize with zeros, then define the input to optimize, where the second column of "input_model" consists of the values of the variable U.

I then simulate for the given time (start time + prediction horizon*sample time = N prediction steps). And store the result of the state trajectory in x_pred and use this variable as well as U to calculate the value of the cost function.

This optimization routine is then called from a script, where I simulate for a given amount of time.

[u_opt] = (solveMPC(Q,R,N,u_min,u_max,x_current,u0,t_start,t_sample))';

However, the result is always an input almost equal zero, which does not happen if I instead simulate the given linear system directly in Matlab with the help of the "lsim" function. Does anyone know if the way I try to do this even works? I would be very thankful for any ansight!

[Balaji]

Can you share your code with the simulink model ?