---
title: "GPU并行线性化误差界：面向非线性和神经网络动力学的实时鲁棒最优控制"
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并行","形式化验证","神经网络动力学","线性化误差界","鲁棒最优控制"]
---

# GPU并行线性化误差界：面向非线性和神经网络动力学的实时鲁棒最优控制

## 速览

本文提出紧致、可微的GPU并行线性化误差界，用于非线性及神经网络动力学的线性时变近似。针对解析动力学引入基于路径的Hessian界；针对神经网络动力学利用NN验证器的仿射松弛和Jacobian校正推导认证误差。扩展GPU并行系统级综合鲁棒控制求解器，支持右可逆干扰矩阵与非零中心干扰集，实现考虑线性化误差的反馈策略在线优化。在168维状态的非线性和神经网络动力学上达到67Hz计算速度，显著降低保守性和求解时间，同时保持形式化保证。

## 关键点

- 提出面向非线性和神经网络动力学的紧致、可微、GPU并行线性化误差界
- 针对解析动力学开发基于路径的Hessian界，针对神经网络动力学利用NN验证器的仿射松弛与Jacobian校正
- 扩展GPU并行系统级综合求解器以支持非零中心干扰集和右可逆干扰矩阵
- 在最高168维状态上实现67Hz鲁棒控制，显著降低保守性和求解时间

## 全文

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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引用前请核对原文;本文由星际流动整理:https://feed.astralor.com/items/itm_c8be365b16ba987a6bdd693d