为非线性与神经网络系统设计实时鲁棒控制，可高效生成严格验证的可达域。
GPU-Parallel Linearization Error Bounds for Real-Time Robust Optimal Control of Nonlinear and Neural Network Dynamics
- 基于路径的海森矩阵与神经网络验证器构建紧致误差界
- 在168维系统上实现高达67Hz的实时控制求解
- 适合需要形式化保证的高维动态系统实时控制场景
本文研究不确定非线性系统的实时鲁棒最优控制问题，其中线性时变（LTV）近似使规划可行，但需可靠的线性化误差界（LEBs）以保障约束满足。我们为非线性与神经网络（NN）动力学的LTV近似开发了紧致、可微分、支持GPU并行的LEBs。针对解析动力学，提出基于路径的海森矩阵界，优于传统区间方法；针对神经网络动力学，利用神经网络验证器生成的仿射松弛与局部雅可比修正，获得可认证的误差界。将基于系统级合成的LTV鲁棒控制求解器扩展为支持右可逆扰动矩阵与非零中心扰动集，实现紧致的区间传播。所提方法GPUSLS-LEO可在在线优化中考虑线性化误差，生成紧致且形式化验证的可达管。在高达168维状态空间的复杂非线性与神经网络动力学上，该方法在GPU上实现最高67Hz的求解速率，相较基线显著降低求解时间与保守性，同时保持形式化保证与实时性能。
原文摘要 · Abstract (English)
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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