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finite-horizon-lqr
Solving finite-horizon LQR via dynamic programming for MPC.
tasks/r2r-mpc-control/environment/skills/finite-horizon-lqr/SKILL.md
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# Finite-Horizon LQR for MPC
## Problem Formulation
Minimize cost over horizon N:
```
J = Σ(k=0 to N-1) [x'Qx + u'Ru] + x_N' P x_N
```
## Backward Riccati Recursion
Initialize: P_N = Q (or LQR solution for stability)
For k = N-1 down to 0: