# MPCGPU: Real-Time Nonlinear Model Predictive Control through Preconditioned Conjugate Gradient on the GPU

arXiv: https://arxiv.org/abs/2309.08079 · HTML: https://mlsanity.com/paper/2309.08079/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2023.

## Built on by (most cited first, 7 of 7)

- [Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2510.06179/) (2025)
- [Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU](https://mlsanity.com/paper/2604.07644/) (2026)
- [CusADi: A GPU Parallelization Framework for Symbolic Expressions and Optimal Control](https://mlsanity.com/paper/2408.09662/) (2024)
- [TurboMPC: Fast, Scalable, and Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2606.24039/) (2026)
- [Machine Learning for Physical Simulation Challenge Results and Retrospective Analysis: Power Grid Use Case](https://mlsanity.com/paper/2505.01156/) (2025)
- [Feedback-MPPI: Fast Sampling-Based MPC via Rollout Differentiation -- Adios low-level controllers](https://mlsanity.com/paper/2506.14855/) (2025)
- [Zero-Shot Function Encoder-Based Differentiable Predictive Control](https://mlsanity.com/paper/2511.05757/) (2025)

## Abstract (arXiv)

Nonlinear Model Predictive Control (NMPC) is a state-of-the-art approach for locomotion and manipulation which leverages trajectory optimization at each control step. While the performance of this approach is computationally bounded, implementations of direct trajectory optimization that use iterative methods to solve the underlying moderately-large and sparse linear systems, are a natural fit for parallel hardware acceleration. In this work, we introduce MPCGPU, a GPU-accelerated, real-time NMPC solver that leverages an accelerated preconditioned conjugate gradient (PCG) linear system solver at its core. We show that MPCGPU increases the scalability and real-time performance of NMPC, solving larger problems, at faster rates. In particular, for tracking tasks using the Kuka IIWA manipulator, MPCGPU is able to scale to kilohertz control rates with trajectories as long as 512 knot points. This is driven by a custom PCG solver which outperforms state-of-the-art, CPU-based, linear system solvers by at least 10x for a majority of solves and 3.6x on average.