# Control Invariant Sets for Neural Network Dynamical Systems and Recursive Feasibility in Model Predictive Control

arXiv: https://arxiv.org/abs/2505.11546 · HTML: https://mlsanity.com/paper/2505.11546/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 43 references that are in the map.
- First posted on arXiv 15 May 2025.

## Builds on (most cited first, 13 of 13)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [Reachability Analysis of Deep Neural Networks with Provable Guarantees](https://mlsanity.com/paper/1805.02242/) (2018)
- [Reach-SDP: Reachability Analysis of Closed-Loop Systems with Neural Network Controllers via Semidefinite Programming](https://mlsanity.com/paper/2004.07876/) (2020)
- [Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms](https://mlsanity.com/paper/2203.07747/) (2022)
- [Safe Control with Neural Network Dynamic Models](https://mlsanity.com/paper/2110.01110/) (2021)
- [Safety Guarantees for Neural Network Dynamic Systems via Stochastic Barrier Functions](https://mlsanity.com/paper/2206.07811/) (2022)
- [Persistently Feasible Robust Safe Control by Safety Index Synthesis and Convex Semi-Infinite Programming](https://mlsanity.com/paper/2209.06896/) (2022)
- [Efficient Interaction-Aware Interval Analysis of Neural Network Feedback Loops](https://mlsanity.com/paper/2307.14938/) (2023)
- [System-level Safety Guard: Safe Tracking Control through Uncertain Neural Network Dynamics Models](https://mlsanity.com/paper/2312.06810/) (2023)
- [Modeling and Control of Diesel Engine Emissions using Multi-layer Neural Networks and Economic Model Predictive Control](https://mlsanity.com/paper/2311.03552/) (2023)
- [Decision-Making for Autonomous Vehicles with Interaction-Aware Behavioral Prediction and Social-Attention Neural Network](https://mlsanity.com/paper/2310.20148/) (2023)

## Abstract (arXiv)

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.