为神经网络动态系统设计安全闭环控制，确保实时可控与长期安全。
Control Invariant Sets for Neural Network Dynamical Systems and Recursive Feasibility in Model Predictive Control
- 用集合递推法生成神经网络模型的控制不变集，保证闭环安全。
- 在模型预测控制中融入不变集，实现安全约束与计算可行性保障。
- 适用于自动驾驶等高安全需求场景，理论与仿真均验证有效。
神经网络是数据驱动建模复杂动态系统的重要工具，提升了控制应用中的预测能力。然而，其内在非线性与黑箱特性给需严格保障安全性和递归可行性的控制设计带来挑战。本文提出针对神经网络动态模型的控制不变集合成算法，采用集合递推方法，在有限步内终止并生成前向不变子集，确保闭环动态持续安全。此外，提出融合控制不变集的模型预测控制设计，通过混合整数优化，保证安全约束的满足与计算层面的递归可行性。本文还进行了全面的理论分析，证明所提方法的性质与保证。数值仿真在自动驾驶场景中展示了方法在离线生成控制不变集、在线实现模型预测控制方面的有效性，确保安全性与递归可行性。
原文摘要 · Abstract (English)
Neural networks are powerful tools for data-driven modeling of complex dynamical systems, enhancing predictive capability for control applications. However, their inherent nonlinearity and black-box nature challenge control designs that prioritize rigorous safety and recursive feasibility guarantees. This paper presents algorithmic methods for synthesizing control invariant sets specifically tailored to neural network based dynamical models. These algorithms employ set recursion, ensuring termination after a finite number of iterations and generating subsets in which closed-loop dynamics are forward invariant, thus guaranteeing perpetual operational safety. Additionally, we propose model predictive control designs that integrate these control invariant sets into mixed-integer optimization, with guaranteed adherence to safety constraints and recursive feasibility at the computational level. We also present a comprehensive theoretical analysis examining the properties and guarantees of the proposed methods. Numerical simulations in an autonomous driving scenario demonstrate the methods' effectiveness in synthesizing control-invariant sets offline and implementing model predictive control online, ensuring safety and recursive feasibility.
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