finite-horizon-lqr

Compute time-varying feedback gains for finite-horizon LQR by using backward Riccati recursion on discrete-time linear system matrices A, B, and cost matrices Q, R to synthesize optimal control actions over a specified horizon N.

Solving a finite-horizon LQR problem requires discrete-time system matrices A and B, cost weighting matrices Q and R, the finite time horizon N, and the initial state x0 to output the initial optimal control input u0.

Backward Riccati recursion works for MPC trajectory stabilization by iterating backwards from the terminal horizon step to dynamically synthesize time-varying LQR feedback gains, applying the first computed control input to forward simulate the system state.

Yes, you can use finite-horizon LQR for robotic path tracking and reference tracking by applying dynamic programming to compute optimal control sequences over the MPC horizon, enabling continuous trajectory stabilization and shaping.

Finite-horizon LQR computes time-varying feedback gains via backward recursion for a specified horizon N, whereas infinite-horizon LQR converges to constant steady-state gains, making the finite approach necessary for MPC reference tracking.

Your MPC controller recalculates feedback gains at every timestep because finite-horizon LQR uses dynamic programming to synthesize time-varying gains over a receding horizon, applying only the first control input before repeating the backward Riccati recursion.