mlsanityData to 7 Oct 2026

Reliably-stabilizing piecewise-affine neural network controllers

arXiv 2111.07183 ↗First posted 13 Nov 2021eess.SY cs.LG cs.SYcited by 13

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Abstract (arXiv)

A common problem affecting neural network (NN) approximations of model predictive control (MPC) policies is the lack of analytical tools to assess the stability of the closed-loop system under the action of the NN-based controller. We present a general procedure to quantify the performance of such a controller, or to design minimum complexity NNs with rectified linear units (ReLUs) that preserve the desirable properties of a given MPC scheme. By quantifying the approximation error between NN-based and MPC-based state-to-input mappings, we first establish suitable conditions involving two key quantities, the worst-case error and the Lipschitz constant, guaranteeing the stability of the closed-loop system. We then develop an offline, mixed-integer optimization-based method to compute those quantities exactly. Together these techniques provide conditions sufficient to certify the stability and performance of a ReLU-based approximation of an MPC control law.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 20 of its 72 references that are in the map. First posted on arXiv 13 Nov 2021.

Builds on

20 of 72 references.

References · 20

  1. 2021Convex optimizationcited by 2,479
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  3. 2016Understanding Deep Neural Networks with Rectified Linear Unitscited by 253
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8 more
  1. 2018Real-time Power System State Estimation and Forecasting via Deep Neural Networkscited by 32
  2. 2019Near-Optimal Rapid MPC using Neural Networks: A Primal-Dual Policy Learning Frameworkcited by 16
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 2; 2024: 3; 2025: 3; 2026: 2.

13 papers.

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  1. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  2. 2022Stability Verification of Neural Network Controllers using Mixed-Integer Programmingcited by 10
  3. 2023Approximate non-linear model predictive control with safety-augmented neural networkscited by 9
  4. 2024Self-Supervised Learning of Iterative Solvers for Constrained Optimizationcited by 3
  5. 2025Improved Scalable Lipschitz Bounds for Deep Neural Networkscited by 2
  6. 2025YANNs: Y-wise Affine Neural Networks for Exact and Efficient Representations of Piecewise Linear Functionscited by 2
  7. 2022Robust stabilization of polytopic systems via fast and reliable neural network-based approximationscited by 1
  8. 2024Mapping back and forth between model predictive control and neural networkscited by 1
  9. 2022An active learning method for solving competitive multi-agent decision-making and control problemscited by 0
  10. 2024A neural network-based approach to hybrid systems identification for controlcited by 0
  11. 2025Geometric Fault-Tolerant Neural Network Tracking Control of Unknown Systems on Matrix Lie Groupscited by 0
  12. 2026ReLU Networks for Model Predictive Control: Network Complexity and Performance Guaranteescited by 0
1 more
  1. 2026Generalization as a robust performance property of learning-enabled dynamical systemscited by 0