# GPU-Parallel Linearization Error Bounds for Real-Time Robust Optimal Control of Nonlinear and Neural Network Dynamics

arXiv: https://arxiv.org/abs/2607.01203 · HTML: https://mlsanity.com/paper/2607.01203/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 35 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 20 of 20)

- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [Funnel Libraries for Real-Time Robust Feedback Motion Planning](https://mlsanity.com/paper/1601.04037/) (2016)
- [Robust adaptive MPC using control contraction metrics](https://mlsanity.com/paper/2209.11713/) (2022)
- [Robust Nonlinear Optimal Control via System Level Synthesis](https://mlsanity.com/paper/2301.04943/) (2023)
- [Safety Beyond the Training Data: Robust Out-of-Distribution MPC via Conformalized System Level Synthesis](https://mlsanity.com/paper/2602.12047/) (2026)
- [Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU](https://mlsanity.com/paper/2604.07644/) (2026)
- [Fast System Level Synthesis: Robust Model Predictive Control using Riccati Recursions](https://mlsanity.com/paper/2401.13762/) (2024)
- [Robustly Constrained Dynamic Games for Uncertain Nonlinear Dynamics](https://mlsanity.com/paper/2509.16826/) (2025)
- [Robust MPC via Min-Max Differential Inequalities](https://mlsanity.com/paper/1611.03924/) (2016)
- [textttimmrax: A Parallelizable and Differentiable Toolbox for Interval Analysis and Mixed Monotone Reachability in JAX](https://mlsanity.com/paper/2401.11608/) (2024)
- [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)
- [Safe Control of Partially-Observed Linear Time-Varying Systems with Minimal Worst-Case Dynamic Regret](https://mlsanity.com/paper/2208.08929/) (2022)
- [Certified Gradient-Based Contact-Rich Manipulation via Smoothing-Error Reachable Tubes](https://mlsanity.com/paper/2602.09368/) (2026)
- [Parallel Differentiable Reachability for Learning and Planning with Certified Neural Dynamics and Controllers](https://mlsanity.com/paper/2605.25346/) (2026)
- [Joint Synthesis of Trajectory and Controlled Invariant Funnel for Discrete-time Systems with Locally Lipschitz Nonlinearities](https://mlsanity.com/paper/2209.03535/) (2022)
- [Robust Model Predictive Control for nonlinear discrete-time systems using iterative time-varying constraint tightening](https://mlsanity.com/paper/2402.13183/) (2024)
- [A Linear Differential Inclusion for Contraction Analysis to Known Trajectories](https://mlsanity.com/paper/2411.11587/) (2024)

## Abstract (arXiv)

This paper studies real-time robust optimal control for uncertain nonlinear systems, where linear time-varying (LTV) approximations make planning tractable but require sound linearization error bounds (LEBs) to guarantee robust constraint satisfaction. We develop tight, differentiable, GPU-parallel LEBs for LTV approximations of nonlinear and neural network (NN) dynamics. For analytic dynamics, we introduce path-based Hessian bounds that are tighter than standard interval methods. For NN dynamics, we derive certified LEBs using NN verifier-generated affine relaxations and local Jacobian corrections. We adapt a GPU-parallel system-level synthesis LTV-based robust control solver to be compatible with these LEBs by extending it to handle right-invertible disturbance matrices and non-zero-centered disturbance sets for tight zonotopic uncertainty propagation. Our method, GPUSLS-LEO, enables online optimization of robust feedback policies that account for linearization error, producing tight, formally verified reachable tubes. On complex nonlinear and NN dynamics up to 168 state dimensions, our method can compute robust control policies on the GPU at rates up to 67 Hz, reducing solve times and conservativeness relative to baselines while preserving formal guarantees and real-time performance.