Hi,
I understand that you want to know how “lqr” algorithm works and how is K matrix computed when A is a variable matrix.
LQR basically decreases the sum of square of errors between the actual state and desired state.
Initial condition is basically initial state of the system. You can input it based on your system.
Refer to the documentation of LQR for more information about this.
Now if A and B are state dependent or variable matrices then the lqr algorithm solves state dependent Riccati equation (SDRE)
LMI is a better tool solve these equations, refer to the documentation below.
Also, refer to this paper to get more information on this topic.
