← 研踪 PaperTrailarXiv:2601.16764 · v2
ReLU Networks for Model Predictive Control: Network Complexity and Performance Guarantees
首次提交 2026-01-23 22:12
版本更新 2026-11-11 19:20
雷达观测 2026-11-13 14:16
摘要
Recent years have witnessed a resurgence in using ReLU neural networks (NNs) to represent model predictive control (MPC) policies. However, determining the sufficient network complexity to ensure closed-loop guarantees 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 project the MPC actions onto a tightened constraint set to satisfy the 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 closed-loop guarantees. To reduce network complexity for the convergence to user-specified target sets, 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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v2 · 2026-11-11 19:20 · 最新观测版本
ReLU Networks for Model Predictive Control: Network Complexity and Performance Guarantees
Recent years have witnessed a resurgence in using ReLU neural networks (NNs) to represent model predictive control (MPC) policies. However, determining the sufficient network complexity to ensure closed-loop guarantees 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 project the MPC actions onto a tightened constraint set to satisfy the 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 closed-loop guarantees. To reduce network complexity for the convergence to user-specified target sets, 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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