# Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU

arXiv: https://arxiv.org/abs/2604.07644 · HTML: https://mlsanity.com/paper/2604.07644/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 56 references that are in the map.
- First posted on arXiv 8 Apr 2026.

## Builds on (most cited first, 30 of 41)

- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions](https://mlsanity.com/paper/2109.06697/) (2021)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [DeepReach: A Deep Learning Approach to High-Dimensional Reachability](https://mlsanity.com/paper/2011.02082/) (2020)
- [How to Train Your Neural Control Barrier Function: Learning Safety Filters for Complex Input-Constrained Systems](https://mlsanity.com/paper/2310.15478/) (2023)
- [Funnel Libraries for Real-Time Robust Feedback Motion Planning](https://mlsanity.com/paper/1601.04037/) (2016)
- [Planning with Learned Dynamics: Probabilistic Guarantees on Safety and Reachability via Lipschitz Constants](https://mlsanity.com/paper/2010.08993/) (2020)
- [FaSTrack: a Modular Framework for Fast and Guaranteed Safe Motion Planning](https://mlsanity.com/paper/1703.07373/) (2017)
- [HPIPM: a high-performance quadratic programming framework for model predictive control](https://mlsanity.com/paper/2003.02547/) (2020)
- [Safe Output Feedback Motion Planning from Images via Learned Perception Modules and Contraction Theory](https://mlsanity.com/paper/2206.06553/) (2022)
- [Learning Barrier Functions for Constrained Motion Planning with Dynamical Systems](https://mlsanity.com/paper/2003.11500/) (2020)
- [A computationally efficient robust model predictive control framework for uncertain nonlinear systems -- extended version](https://mlsanity.com/paper/1910.12081/) (2019)
- [Convex synthesis and verification of control-Lyapunov and barrier functions with input constraints](https://mlsanity.com/paper/2210.00629/) (2022)
- [Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systems](https://mlsanity.com/paper/2104.08695/) (2021)
- [Bridging the Gap Between Safety and Real-Time Performance in Receding-Horizon Trajectory Design for Mobile Robots](https://mlsanity.com/paper/1809.06746/) (2018)
- [Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systems](https://mlsanity.com/paper/2212.06874/) (2022)
- [TinyMPC: Model-Predictive Control on Resource-Constrained Microcontrollers](https://mlsanity.com/paper/2310.16985/) (2023)
- [Robust Tracking with Model Mismatch for Fast and Safe Planning: an SOS Optimization Approach](https://mlsanity.com/paper/1808.00649/) (2018)
- [Primal-Dual iLQR for GPU-Accelerated Learning and Control in Legged Robots](https://mlsanity.com/paper/2506.07823/) (2025)
- [Robust Nonlinear Optimal Control via System Level Synthesis](https://mlsanity.com/paper/2301.04943/) (2023)
- [MPCGPU: Real-Time Nonlinear Model Predictive Control through Preconditioned Conjugate Gradient on the GPU](https://mlsanity.com/paper/2309.08079/) (2023)
- [ReLU-QP: A GPU-Accelerated Quadratic Programming Solver for Model-Predictive Control](https://mlsanity.com/paper/2311.18056/) (2023)
- [Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2510.06179/) (2025)
- [Safety Beyond the Training Data: Robust Out-of-Distribution MPC via Conformalized System Level Synthesis](https://mlsanity.com/paper/2602.12047/) (2026)
- [Robust Model Predictive Control with Polytopic Model Uncertainty through System Level Synthesis](https://mlsanity.com/paper/2203.11375/) (2022)
- [CusADi: A GPU Parallelization Framework for Symbolic Expressions and Optimal Control](https://mlsanity.com/paper/2408.09662/) (2024)
- [Using Neural Networks to Compute Approximate and Guaranteed Feasible Hamilton-Jacobi-Bellman PDE Solutions](https://mlsanity.com/paper/1611.03158/) (2016)
- [Fast System Level Synthesis: Robust Model Predictive Control using Riccati Recursions](https://mlsanity.com/paper/2401.13762/) (2024)

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

- [Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control](https://mlsanity.com/paper/2604.19018/) (2026)
- [Pixels to Proofs: Probabilistically-Safe Latent World Model Control via Parallel Conformal Robust MPC](https://mlsanity.com/paper/2606.15594/) (2026)
- [VISION-SLS: Safe Perception-Based Control from Learned Visual Representations via System Level Synthesis](https://mlsanity.com/paper/2604.24894/) (2026)
- [Robustness without Wrinkles: Parallel Simulation and Robust MPC for Certified Deformable Manipulation](https://mlsanity.com/paper/2606.14188/) (2026)
- [Steering Robustness into World Action Models via Mechanistic Interpretability and Optimal Control](https://mlsanity.com/paper/2607.14943/) (2026)
- [TurboMPC: Fast, Scalable, and Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2606.24039/) (2026)
- [GPU-Parallel Linearization Error Bounds for Real-Time Robust Optimal Control of Nonlinear and Neural Network Dynamics](https://mlsanity.com/paper/2607.01203/) (2026)

## Abstract (arXiv)

We present GPU-SLS, a GPU-parallelized framework for safe, robust nonlinear model predictive control (MPC) that scales to high-dimensional uncertain robotic systems and long planning horizons. Our method jointly optimizes an inequality-constrained, dynamically-feasible nominal trajectory, a tracking controller, and a closed-loop reachable set under disturbance, all in real-time. To efficiently compute nominal trajectories, we develop a sequential quadratic programming procedure with a novel GPU-accelerated quadratic program (QP) solver that uses parallel associative scans and adaptive caching within an alternating direction method of multipliers (ADMM) framework. The same GPU QP backend is used to optimize robust tracking controllers and closed-loop reachable sets via system level synthesis (SLS), enabling reachability-constrained control in both fixed- and receding-horizon settings. We achieve substantial performance gains, reducing nominal trajectory solve times by 97.7% relative to state-of-the-art CPU solvers and 71.8% compared to GPU solvers, while accelerating SLS-based control and reachability by 237x. Despite large problem scales, our method achieves 100% empirical safety, unlike high-dimensional learning-based reachability baselines. We validate our approach on complex nonlinear systems, including whole-body quadrupeds (61D) and humanoids (75D), synthesizing robust control policies online on the GPU in 20 milliseconds on average and scaling to problems with 2 x 10^5 decision variables and 8 x 10^4 constraints. The implementation of our method is available at https://github.com/Jeff300fang/gpu_sls.