Hi,

the standard form of a quadratic optimal control problem is given by

J = 1/2 * integration (x'*Q*x + u'*R*u) {dt},

where Q and R are weight matrices.

If we consider a second-order system with one input, Q is a 2 by 2 matrix and R is a scalar. For example, we can select Q = 100*eye(2) and R = 1.

My question is the following: If we select Q = 1*eye(2) and R = 0.01, then will the result be different from the case when Q = 100*eye(2) and R = 1? I thought that there would be no difference because the cost function J will differ by only a scale factor 0.01. But when I took a simple example to check if this is true, I found that the two results are a little different. Could anyone explain why the two cases are not the same?

Thank you very much.