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.
Ivo Houtzager (2021). DPLQR (https://www.mathworks.com/matlabcentral/fileexchange/19120-dplqr), MATLAB Central File Exchange. Retrieved .
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