这篇论文把鲁棒控制加速到67 Hz，处理168维非线性动力学的车，GPUSLS-LEO在GPU上跑得比现有方法更快更紧，适合搞实时控制的人。
本文提出GPUSLS-LEO方法，为非线性与神经网络动力学系统的线性时变（LTV）近似提供紧致、可微、GPU并行的线性化误差界（LEBs）。针对解析动力学，引入基于路径的Hessian界，比标准区间方法更紧；针对神经网络动力学，通过NN验证器生成的仿射松弛和局部雅可比修正导出认证LEBs。该方法在高达168维状态的非线性与神经网络动力学系统上，以67 Hz的速率在GPU上计算鲁棒控制策略，相比基线降低了求解时间和保守性，同时保持形式化保证和实时性能。
GPU-Parallel Linearization Error Bounds for Real-Time Robust Optimal Control of Nonlinear and Neural Network Dynamics
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.