首次给出ReLU网络逼近MPC策略的复杂度边界，保障闭环性能。
ReLU Networks for Model Predictive Control: Network Complexity and Performance Guarantees
- 基于投影法强制硬约束，建立状态相关利普希茨连续性
- 首次推导出保证闭环性能所需的网络宽度与深度显式上界
- 提出状态感知的非均匀误差框架，降低网络复杂度
近年来，使用ReLU神经网络（NN）表示模型预测控制（MPC）策略重新兴起。然而，确定确保闭环性能所需的网络复杂度仍是一个基本开放问题。这涉及关键的精度-复杂度权衡：网络过小可能无法捕捉MPC策略，过大则可能抵消ReLU网络近似的收益。本文提出一种基于投影的方法以强制实现硬约束，并建立了最优MPC代价函数的状态依赖利普希茨连续性，从而实现闭环系统的精确收敛分析。首次推导出保证闭环性能所需的ReLU网络宽度与深度的显式上界。为进一步降低网络复杂度并提升闭环性能，提出一种非均匀误差框架，采用状态感知缩放函数自适应调整网络输入与输出。本工作为可验证的基于ReLU NN的MPC提供了基础性进展。
原文摘要 · Abstract (English)
Recent years have witnessed a resurgence in using ReLU neural networks (NNs) to represent model predictive control (MPC) policies. However, determining the required network complexity to ensure closed-loop performance remains a fundamental open problem. This involves a critical precision-complexity trade-off: undersized networks may fail to capture the MPC policy, while oversized ones may outweigh the benefits of ReLU network approximation. In this work, we propose a projection-based method to enforce hard constraints and establish a state-dependent Lipschitz continuity property for the optimal MPC cost function, which enables sharp convergence analysis of the closed-loop system. For the first time, we derive explicit bounds on ReLU network width and depth for approximating MPC policies with guaranteed closed-loop performance. To further reduce network complexity and enhance closed-loop performance, we propose a non-uniform error framework with a state-aware scaling function to adaptively adjust both the input and output of the ReLU network. Our contributions provide a foundational step toward certifiable ReLU NN-based MPC.
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