FORC · Lecture 7

Constrained model predictive control

Simeon Nedelchev

Receding horizon

Solve from the measured state.

Apply the first control.

Shift the plan and solve again at the next tick.

\min \sum_{k=0}^{N-1}(x_k^\top Qx_k+u_k^\top Ru_k)+x_N^\top P_fx_N

Dynamics, input limits, and state limits define feasibility.

$v=2$ m/s, maximum braking $a=1$ m/s $^2$

d_{\rm stop}=\frac{v^2}{2a}=2\ {\rm m}

A wall 1 m away makes collision avoidance infeasible.

Infeasible model, short horizon, and numerical failure are different diagnoses.

Record status and residuals.

The core example controls height and vertical speed.

Thrust limits become acceleration bounds around hover.

The take-home extends to attitude dynamics.

MPC and clipped LQR use identical limits.

Compare violations, tracking, and computation time.