Simulates a 1D point mass controlled using LQR with input constraints. Solving the constrained quadratic program (LQR QP) can in many cases do better than simply thresholding the output of an unconstrained LQR controller.
When following a reference that approaches input constraints, state feedback noise can make the thresholded LQR suboptimal. The quadratic program LQR is again better here.
Run constrained_lqr.py. Pass --ref to follow a bang bang reference and --noise to inject noise into the state feedback.
Change w_pos, w_vel, max_abs_u, and N to experiment with different cost functions, input constraints, and horizon lengths.
- numpy
- matplotlib
- one of scipy or qpoases' Python interface to solve the quadratic program. qpoases runs much faster and is recommended.
If you get an undefined symbol error when using qpoases, see https://projects.coin-or.org/qpOASES/ticket/70.