finite-horizon-lqr SKILL.md skillA
finite-horizon-lqr from benchflow-ai/benchflow is an agent skill: a SKILL.md folder an AI agent loads when a task calls for it.
mdr add benchflow-ai/benchflow/finite-horizon-lqr@git:20260610.e2a435fPins git:20260610.e2a435f in mdr.lock. Pin the fingerprint instead.
- Audit grade
- A, 17 of 17 checks passed
- Kind
- SKILL.md skill
- Repository
- benchflow-ai/benchflow
- Path
tests/fixtures/skillsbench_slice/r2r-mpc-control/environment/skills/finite-horizon-lqr/SKILL.md- Versions recorded
- 1
- Latest version
- git:20260610.e2a435f, committed Jun 10, 2026
- Size
- 1,078 bytes
- Repository stars
- 359
- License
- Apache-2.0
Solving finite-horizon LQR via dynamic programming for MPC.
Collected from public GitHub. Every version is saved exactly as it was and never changes. Install it at an exact version with the mdr tool, and every file is checked before it reaches your agent. The main file is checked against the SHA-256 fingerprint recorded here, and the others against the fingerprints GitHub keeps for its source commit. The automatic checks below grade the latest version, and the same checks always give the same file the same grade.
What the file says
# 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:
```python
K_k = inv(R + B'P_{k+1}B) @ B'P_{k+1}A
P_k = Q + A'P_{k+1}(A - B @ K_k)
```
## Forward Simulation
Starting from x_0:
```python
u_k = -K_k @ x_k
x_{k+1} = A @ x_k + B @ u_k
```
## Python Implementation
```python
def finite_horizon_lqr(A, B, Q, R, N, x0):
nx, nu = A.shape[0], B.shape[1]
K = np.zeros((nu, nx, N))
P = Q.copy()
# Backward pass
for k in range(N-1, -1, -1):
K[:,:,k] = np.linalg.solve(R + B.T @ P @ B, B.T @ P @ A)
P = Q + A.T @ P @ (A - B @ K[:,:,k])
# Return first control
return -K[:,:,0] @ x0
```
## MPC Application
At each timestep:
1. Measure current state x
2. Solve finite-horizon LQR from x
3. Apply first control u_0
4. Repeat next timestepRead the whole file at its exact version.
How to install
mdr add benchflow-ai/benchflow/finite-horizon-lqr@sha256:8ce87c503270a401The line at the top of this page pins the label git:20260610.e2a435f, which is what most people want. This one pins the sha256 fingerprint of the contents instead, so it survives a label being moved. Either way the exact version is written to mdr.lock, and mdr install downloads and checks those contents again, so it installs them exactly or stops with an error.
[](https://markdownregistry.com/a/art_v5ox57jiylejegdo)
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Versions
The registry has recorded 1 version of this file, committed on Jun 10, 2026.
Audit of the latest version
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Source
benchflow-ai/benchflow · 359 stars · license Apache-2.0 · pushed 2026-10-30 · branch main
API
GET https://markdownregistry.com/api/v1/artifacts/art_v5ox57jiylejegdo GET https://markdownregistry.com/api/v1/resolve?ref=benchflow-ai/benchflow/finite-horizon-lqr GET https://markdownregistry.com/api/v1/blob/8ce87c503270a401f9bce17518a8f11d8cc421de2f15984678ddeb0b8c27575f
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