ReLU Networks for Model Predictive Control: Network Complexity and Performance Guarantees

• URL: http://arxiv.org/abs/2601.16764v1
• Date: Fri, 23 Jan 2026 14:12:10 GMT
• Title: ReLU Networks for Model Predictive Control: Network Complexity and Performance Guarantees
• Authors: Xingchen Li, Keyou You,
• Abstract summary: We propose a projection-based method to enforce hard constraints and establish a state-dependent Lipschitz continuity property for the optimal MPC cost function.<n>For the first time, we derive explicit bounds on ReLU network width and depth for approximating MPC policies with guaranteed closed-loop performance.
• Score: 10.106606525540688
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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