---
title: "GPU-Parallel Linearization Error Bounds for Real-Time Robust Optimal Control of Nonlinear and Neural Network Dynamics"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2607.01203v1"
permalink: "https://feed.astralor.com/items/itm_c8be365b16ba987a6bdd693d"
published: "2026-07-01T17:42:37.000Z"
score: 56
channel: "ai"
tags: ["GPU parallelism","Formal Verification","neural network dynamics","linearization error bounds","robust optimal control"]
---

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

## At a glance

This paper proposes tight, differentiable GPU-parallel linearization error bounds (LEBs) for LTV approximations of nonlinear and neural network dynamics. For analytic dynamics, path-based Hessian bounds are introduced; for NN dynamics, certified LEBs are derived using affine relaxations from NN verifiers and local Jacobian corrections. The GPU-parallel system-level synthesis LTV robust control solver is extended to handle right-invertible disturbance matrices and non-zero-centered disturbance sets, enabling online optimization of robust feedback policies accounting for linearization error. On nonlinear and NN dynamics up to 168 state dimensions, the method achieves 67Hz GPU computation, reducing solve times and conservativeness while preserving formal guarantees and real-time performance.

## Key points

- Proposes tight, differentiable, GPU-parallel linearization error bounds for nonlinear and neural network dynamics
- Develops path-based Hessian bounds for analytic dynamics and certified LEBs using NN verifier affine relaxations and local Jacobian corrections
- Extends GPU-parallel system-level synthesis solver to handle non-zero-centered disturbance sets and right-invertible disturbance matrices
- Achieves 67Hz robust control on up to 168-dimensional dynamics, reducing conservativeness and solve time

## Full text

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.

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