optimization: calling fmincon in Simulink (embedded block)

Hello,

I am going to implement a model predictive controller in Simulink. Therefore I need to solve a constrained optimization problem, thus finding the vector that mimimises a certain multi-variable function, subject to constraints. (I do know there is a MPC block in Simulink, but I need to implement it myself as part of a bigger Simulink model).

In Matlab this is possible using fmincon. So I tried using an embedded Matlab block in Simulink where fmincon was called, but this does not work. I also tried "coder.extrinsic('fmincon')" code but that did not work.

Can anybody tell me if it is possible to use fmincon in a SIMULINK model (thus not working in a .m Matlab file) or if there are alternatives? Or do I have to try to implement the algebra behind this function (quadratic programming etc.) in Simulink myself?

All help appreciated! Maarten

[Khalid]

I know this is from a while ago, but I would like to +1 this question. I have a very similar problem to Maarten.

Like Maarten I tried using coder.extrinsic('fmincon') from within the MATLAB Function block within simulink; but it is then not possible to pass handles to an extrinsic function (which is needed to be able to run fmincon).

Is there another/better way to perform constrained optimisation within a Simulink model (i.e. where it needs to be run once per time-step). I am familiar with using constrained optimisation of Simulink model parameters (i.e. where Simulink is called once per objective function evaluation); but here we seek to run the Simulink model only once, but run the optimisation once per time-step.

The approach Maarten and I have taken seems like the 'obvious' one but doesn't work. Any pointers gratefully received.

- Khalid.

Answer 1

[Matteo Ragni]

I will post the same answer I gave on Stack Overflow on the same topic

You need to call the optimal problem function with coder.extrinsic.

Instead of using coder.extrinsic on the fmincon function, I usually write a wrapper for the optimization problem that I have to solve as a .m file function for Matlab (namely opt_problem) and declare coder.extrinsic('opt_problem') in the simulink Matlab function. I'll give you a simple example:

Consider this Simulink "model", in which at each integration step I want to solve a linear regression problem on some generated data. The optimization problem is something in the form:

minimize (y - m x - q)²
subject to  0 ≤ m ≤ 1
            0 ≤ q ≤ 1

The scheme is really simple, bet the regressor calls fmincon:

Let's see inside the regressor:

function [m, q] = regressor(xs, ys, mic, qic)
  coder.extrinsic('opt_problem'); % <- Informing the Coder
  m = 0;
  q = 0;
  [m, q] = opt_problem(xs, ys, mic, qic); % <- Optimal problem wrapper call
end

this function is only a wrapper for an external function `opt_problem`. Let'see it (it has two functions inside):

function [m, q] = opt_problem(xs, ys, mic, qic)
  fmincon_target = @(mq)(target(mq, xs, ys));
  mq = fmincon(fmincon_target, [mic; qic], [], [], [], [], [0; 0], [1; 1]);
  m = mq(1);
  q = mq(2);
end

function r = target(mq, xs, ys)
  r = norm(ys - xs.*mq(1) - mq(2));
end

and that's all. As you can see in the picture, the scheme runs and the solution are the m, q parameters (in the two displays) that minimize the target function while respecting the constraints (m = 1.2 → m_opt = 1).

[F R]

Hi @Matteo Ragni, I have similar problem, but the difference is that I am using m and q values in the rest of my simulation as gains, where the cost function r is dependable on the results from there (r is indirectly dependant on m and q). So, my question is how do I define m and q to be updated in each optimization run in the rest of the Simulink file? and should I define initial values for them?

[Giovanni Palmieri]

Hi Matteo, what is inside the Linear Trasformation with Noise block??

[manish kumar]

@Matteo Ragni how to add constraint function on m and q please help me writing code

[Farshid R]

Hello @ manish kumar

Were you able to solve your problem?

I have a similar problem.

[Kartikaya]

What is meant by external function , where it is placed ?