Dear Kailas Naresh,

It is the other way around. Minimizing the objective function J affects the controller gain K. Your aim in LQR is to find a K which minimizes J.

Saying that, the explanation from Harald Kirchsteiger offers a decent explanation.

Regards,

Guru

Dear Kailas Naresh,

First of all I must say that I completely agree with the explanations given by the colleague Harald Khandavalli and I add.

The control law for an LQR regulator is of the form:

u (t) = -Kx (t)

And the expression giving the gain matrix K is:

K = R-1 BT P

So the link between the cost function 'J' and the gain is the matrix R of weighting of the control energy, the choice of matrices R and Q is to find a compromise the best possible according to the desired performance.

Best regards