finite-horizon-lqr

finite-horizon-lqr is a skill for Claude Code, Codex from benchflow-ai/skillsbench. It costs 19 tokens per session (392 once invoked), scanned A, original, Apache-2.0.

A guide to solving finite-horizon linear-quadratic regulation, or LQR, as part of model predictive control, or MPC. LQR chooses control actions by balancing system performance against control effort over a fixed number of steps.

In plain words
What is it for?
Use it to implement the Riccati recursion, simulate the controlled system, and apply the first action repeatedly at each time step.
Why use it?
It provides the backward and forward calculations needed to compute an MPC control action for a changing system state.

Skill for Claude CodeCodex

Written for no agent in particular: nothing here depends on one.

Good fit Use it to implement the Riccati recursion, simulate the controlled system, and apply the first action repeatedly at each time step.

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Install with agentmods
npx agentmods add skills/benchflow-ai/skillsbench/finite-horizon-lqr
About the project

SkillsBench is a benchmark for measuring how effectively AI agents use modular skills—folders containing instructions, scripts, and resources—to complete specialized tasks. It helps researchers and developers evaluate both skill quality and agent behavior, including tasks that require combining multiple skills. The catalogue’s skills and instructions are evaluated as part of this workflow.

benchflow-ai/skillsbench · 1,764 stars · on GitHub · skillsbench.ai

Install

Getting it into your agent

One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.

Any agent
npx skills add benchflow-ai/skillsbench --skill finite-horizon-lqr
Clone the repo
git clone --depth 1 https://github.com/benchflow-ai/skillsbench

Made for: Claude Code, Codex.

Wrote this? Show the measurements

A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.

agentmods badge for finite-horizon-lqr

README.md
[![agentmods](https://agentmods.dev/badge/skills/benchflow-ai/skillsbench/finite-horizon-lqr/github.svg)](https://agentmods.dev/skills/benchflow-ai/skillsbench/finite-horizon-lqr)
Your own site
<a href="https://agentmods.dev/skills/benchflow-ai/skillsbench/finite-horizon-lqr"><img src="https://agentmods.dev/badge/skills/benchflow-ai/skillsbench/finite-horizon-lqr/github.svg" alt="Measured on agentmods" height="20"></a>

Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.

agentmods 80×15 button for finite-horizon-lqr

Your own site · 80×15
<a href="https://agentmods.dev/skills/benchflow-ai/skillsbench/finite-horizon-lqr"><img src="https://agentmods.dev/badge/skills/benchflow-ai/skillsbench/finite-horizon-lqr.svg" alt="Reviewed on agentmods" width="80" height="20"></a>
Per session 19 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 392 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. A grade says what 26 rules found in the file — not that it is safe. Third-party audits
  • NVIDIA SkillSpector pass 7 Sept 2026
How audits are shown
Origin original No closer match found in the catalogue.
Token cost

What it costs to keep this loaded

Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.

ModelPer sessionOnce invoked
Fable 5.1 $0.00019 $0.00392
Opus 5 $0.00010 $0.00196
Sonnet 5 $0.00004 $0.00078
Haiku 4.5 $0.00002 $0.00039

Measured 9d ago against content hash 8ce87c503270, method: parsed. Prices are Anthropic first-party input rates as of 2026-09-12, from the pricing page.

Security

Grade A, and why

finite-horizon-lqr scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 9d ago.

A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.

Nothing flagged

None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.

Origin

Copies of this mod

1 near-identical copy found in the catalogue:

tasks/r2r-mpc-control/environment/skills/finite-horizon-lqr/SKILL.md · 57 lines

What it actually 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:

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:

u_k = -K_k @ x_k
x_{k+1} = A @ x_k + B @ u_k

Python Implementation

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 timestep
Changes

What this file has done since we first saw it

Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.

  1. 9d ago First seen · 57 lines · 19 tokens per session scan A 8ce87c503270

Subscribe to this mod's changes

finite-horizon-lqr is a skill published in the GitHub repository benchflow-ai/skillsbench (1,764 stars, last pushed 1mo ago), licensed Apache-2.0. It adds 19 tokens to every session and 392 once invoked, about $0.0001 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-09-03.

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