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

2026-04-08

AI Summary

This work addresses the challenge of real-time, safe, and robust model predictive control for high-dimensional uncertain nonlinear systems over long horizons. The authors propose a GPU-parallelized System Level Synthesis (SLS) framework that, for the first time, embeds reachability constraints directly into the SLS formulation and jointly optimizes the nominal trajectory, tracking controller, and closed-loop reachable set. By integrating sequential quadratic programming, an ADMM-accelerated QP solver, associative scanning, and adaptive caching, the method generates online control policies in under 20 milliseconds on average for systems with 61–75 states, handling up to 2×10⁵ variables and 8×10⁴ constraints. Compared to CPU and GPU baselines, it achieves 97.7% and 71.8% speedups in nominal trajectory computation, respectively, and a 237× acceleration in SLS and reachability calculations, enabling millisecond-scale, scalable, and empirically 100% safe nonlinear MPC.

Abstract

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.

Problem

• nonlinear MPC
• robust control
• reachability
• GPU acceleration
• high-dimensional systems

Innovation

• GPU-accelerated MPC
• System Level Synthesis
• Reachability-constrained control
• Parallel QP solver
• Robust nonlinear control