Talk:Linear–quadratic regulator

Inconsistent time indices
For the section "Finite-horizon, discrete-time LQR", the cost metric involves :$$u_0$$, which is not defined in the formulation since :$$u_k = -F_k x_{k-1} \,$$ and :$$u_0 = -F_0 x_{-1} \,$$ and $$ x_{-1} $$ is not specified.

I propose using the dynamics and performance metric parallel to the infinize-horizon case:


 * $$x_{k+1} = A x_k + B u_k \,$$
 * $$J = \sum\limits_{k=0}^{N-1} \left( x_k^T Q x_k + u_k^T R u_k \right) + x_N^T Q x_N $$

Intellec7 (talk) 16:50, 9 April 2012 (UTC)

Wrong meaning
In the article it is stated that: u = -Kx. This is true but it should be said that there is another variable u' that is the new input. Moreover, this u' input is the wanted state of the variable that is linked to the biggest eigenvalue of Q. Example: Let's say that dx/dt=Ax+Bu where u is newtons and x=(postition, velocity, acceleration). if
 * $$\mathbf{Q} =

\begin{bmatrix} 500 & 0 & 0 \\ 0 & 10 & 0 \\ 0 & 0 & 0 \end{bmatrix}. $$

then the new system dx/dt = Ax + B(u' - kx), u' is the postition to control because it is the first value of the state vector x and its eigenvalue in Q is the biggest (500 > 10). So, the newtons applied to B are u' - kx. I don't know if it is possible to control other variables (velocity and acceleration) to reach a value different from zero. I am not an expert in control, so someone with a good knowlodge of the subject should modify the article. —Preceding unsigned comment added by 89.140.190.252 (talk) 07:03, 6 April 2010 (UTC)

Errors
What is "alogarithm"? Is it a misspelling for "algorithm"?

As far as I understand, there is an error in the equation: $$F = -R B^{T} P x_{k}$$ it should be replaced by: $$F = -R B^{T} P$$ or does the feedback constant really depend on the state?


 * Thanks - the Kalman gain does not depend on the state. --Jiuguang Wang (talk) 16:19, 5 July 2008 (UTC)

Links to Riccati equation
Could someone please write a page on the matrix Riccati equation, instead of simply linking to the Riccati differential equation. The connection between them isn't obvious. LachlanA (talk) 00:07, 22 January 2008 (UTC)

Requested move 26 October 2016

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section. 

The result of the move request was: Handling as an uncontroversial request. (non-admin closure) — Andy W. ( talk ) 02:44, 28 October 2016 (UTC)

Linear-quadratic regulator → Linear–quadratic regulator – This term should make use of an en-dash and not a hyphen. For some reason though, I don't seem to be able to make the move myself; perhaps Wikipedia considers the two titles identical. If that is the case, this behavior should be changed so that Wikipedia doesn't consider the two titles to be identical (because they're not). —Kri (talk) 16:32, 26 October 2016 (UTC)


 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.