DPLQR

Nonsteady LQ state-feedback gain design with final state penalty

The m-file "dplqr" which solves the discrete nonsteady-state optimal control problem by a backwards iteration. The problem is to find K[n] in the state-feedback u[n] = -K[n]x[n], and minimizes

J = 0.5*sum(x[n]'Qx[n] + u[n]'Ru[n]) + 0.5*x[N]'Fx[N]

subject to x[n+1] = Ax[n] + Bu[n] with n = 0...N-1.

The inclusion of the x[N]'Fx[N] implies the desire to reach the final state as close as possible. Compared to "normal"
LQR/LQG design where the weighing matrices Q and R needs to be given at the input, this function requires also that the final-state weighing matrix F is given at the input.