Originally posted by: michelco

Hello

I need some help constructing the Q,l and r matrices for a circular constraint using cplexqcp in an MPC application. 

The constraint is: (x-x_ref)^2 + (y-y_ref)^2 <= w, where w is the radius of the circle. The system has 7 states, 4 inputs and a slack variable and a prediction horizon of 30, thus the decision variable has (7+4+1)*30 = 360 variables. Since the reference is changing at each step in the horizon I should get 30 constraints, of the form given above (just a slightly different value for the ref's at each step). I just can't seem to construct the matrices correctly, r becoms 30x1, l 30x360 but Q becomes 360x360 which cplexqcp deems to be wrong (which it probably is). Anyone can help me out a little bit?

Best regards MC 

If I understood correctly you are building up 30 different constrains (r is 30x1). This means Q should be a cell array with one matrix for each constraint, not a single flat matrix.

Not sure this is an option but it might be easier to use the Class API and use function addQCs to add the constraints one by one.

Originally posted by: michelco

Thank you! I've changed the Q matrix to a cell matrix, but it still gives me the same error "error: incorrect l,Q,r.". I'm using cplexqcp within Matlab by the way. I also tried changing r to a row vector (1x30) but to no avail. I'm guessing it's something wrong with l ?

Never mind, I had forgotten to transpose l. Appreciate the answer though because, it helped me since I didnt realize Q was supposed to be a cell matrix ,so thank you again!

For sake of completeness and future reference, here is a version of the cplexqcp.m example shipped with CPLEX that just adds the same quadratic constraint twice:

   % Add two identical quadratic constraints. Both only have a quadratic
   % part. The linear part is all-zero
   % l has one column for each constraint   
   l = [0 0;
        0 0;
        0 0];
   % r has one column for each constraint
   r = [1 1];
   % Q has one cell for each constraint, each cell is a matrix
   Q = { [1  0  0
          0  1  0
          0  0  1], ...
         [1  0  0
          0  1  0
          0  0  1] };

The important point (that is unfortunately not explicit in the docs) is that Q must be a row of cells.