用数学证明让Transformer在无人机控制中稳定可靠
Stable Transformer-Actor-Critic Model Predictive Control: A Contraction Analysis Approach
- 用增量输入-状态稳定性理论证明Transformer可全局稳定
- 结合黎曼收缩理论分析物理系统与神经网络的联动稳定性
- 在3D无人机任务中实现避障和目标追踪的可验证鲁棒控制
Actor-Critic模型预测控制（MPC）能有效应对复杂非凸控制问题，但保障基于序列的学习模型在闭环系统中的稳定性仍具挑战。本文提出一种新型的Transformer-Actor-Critic MPC架构，并提供严格的鲁棒性保证。首先，证明Transformer网络满足全局增量输入-状态稳定性（δISS）。随后，利用黎曼收缩理论分析物理系统与预测神经网络之间的耦合动态。最后，将这些理论边界作为训练正则项，生成可验证鲁棒的控制策略。该框架在非线性三维无人机模型上进行了验证，实现了目标到达与障碍物避让等任务。
原文摘要 · Abstract (English)
Actor-Critic Model Predictive Control (MPC) effectively addresses complex, non-convex control problems, but guaranteeing the closed-loop stability of sequence-based learning models within these pipelines remains challenging. This paper introduces a novel Transformer-Actor-Critic MPC architecture with formal robustness guarantees. First, we prove that Transformer networks can satisfy global incremental Input-to-State Stability ($δ$ISS). We then leverage Riemannian contraction theory to analyze the interconnected dynamics between the physical plant and the predictive neural network. Finally, we integrate these theoretical bounds as a training regularizer to yield a certifiably robust policy. The framework is validated on a nonlinear 3D drone model executing target-reaching and obstacle-avoidance maneuvers.
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