Error in control input for larger noise levels

[CheeGY]

Hi!

First of all, thanks for this repository! I think it is very useful for anyone who is starting to get in touch with tube-based MPC.

I was testing out the example in the repository and notice something peculiar. When I set the noise level from 0.15 to 0.2, i.e.,
from:
W_vertex = [0.15, 0.15; 0.15, -0.15; -0.15, -0.15; -0.15, 0.15];
to:
vertex_max = 0.2;
W_vertex = [vertex_max, vertex_max; vertex_max, -vertex_max; -vertex_max, -vertex_max; -vertex_max, vertex_max];

I observe that
(i) the values of the final control input (u0 + K(x-x0)) exceed the constraint set (Uc) in the first timestep, and
(ii) the values of the nominal control input (u0) exceed the robust constraint set (Uc_robust) in the first timestep.

Here is a plot of the time histories of the final and nominal control inputs. The blue line is the final control input and the red line is the nominal control input. The control limits are at [-1, 1].

I think we should expect the final control input to stay within Uc, is that correct?

Hope to hear from you and happy to discuss. Thanks!

[HiroIshida]

@CheeGY Thanks for your report!
Currently I don't have time to fix the problem. Any help including making PR would be really welcome.