# Topological Feasibility Guarantees for Differentiable Predictive Control

arXiv: https://arxiv.org/abs/2608.10332 · HTML: https://mlsanity.com/paper/2608.10332/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 76 references that are in the map.
- First posted on arXiv 11 Aug 2026.

## Builds on (most cited first, 30 of 35)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems](https://mlsanity.com/paper/1705.01292/) (2017)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Learning-based Model Predictive Control for Safe Exploration](https://mlsanity.com/paper/1803.08287/) (2018)
- [A predictive safety filter for learning-based control of constrained nonlinear dynamical systems](https://mlsanity.com/paper/1812.05506/) (2018)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [Efficient representation and approximation of model predictive control laws via deep learning](https://mlsanity.com/paper/1806.10644/) (2018)
- [Learning an Approximate Model Predictive Controller with Guarantees](https://mlsanity.com/paper/1806.04167/) (2018)
- [Enforcing robust control guarantees within neural network policies](https://mlsanity.com/paper/2011.08105/) (2020)
- [Learning Model Predictive Control for iterative tasks. A Data-Driven Control Framework](https://mlsanity.com/paper/1609.01387/) (2016)
- [Data-Driven Model Predictive Control with Stability and Robustness Guarantees](https://mlsanity.com/paper/1906.04679/) (2019)
- [Deep Learning Alternative to Explicit Model Predictive Control for Unknown Nonlinear Systems](https://mlsanity.com/paper/2011.03699/) (2020)
- [A computationally efficient robust model predictive control framework for uncertain nonlinear systems -- extended version](https://mlsanity.com/paper/1910.12081/) (2019)
- [Automatic nonlinear MPC approximation with closed-loop guarantees](https://mlsanity.com/paper/2312.10199/) (2023)
- [Approximate non-linear model predictive control with safety-augmented neural networks](https://mlsanity.com/paper/2304.09575/) (2023)
- [Safe Physics-Informed Machine Learning for Dynamics and Control](https://mlsanity.com/paper/2504.12952/) (2025)
- [Differentiable Safe Controller Design through Control Barrier Functions](https://mlsanity.com/paper/2209.10034/) (2022)
- [Predictive safety filter using system level synthesis](https://mlsanity.com/paper/2212.02111/) (2022)
- [Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach](https://mlsanity.com/paper/2208.02319/) (2022)
- [Regularized and Distributionally Robust Data-Enabled Predictive Control](https://mlsanity.com/paper/1903.06804/) (2019)
- [A nonlinear model predictive control framework using reference generic terminal ingredients -- extended version](https://mlsanity.com/paper/1909.12765/) (2019)
- [Feasibility and Regularity Analysis of Safe Stabilizing Controllers under Uncertainty](https://mlsanity.com/paper/2301.04603/) (2023)
- [State-action control barrier functions: Imposing safety on learning-based control with low online computational costs](https://mlsanity.com/paper/2312.11255/) (2023)
- [Robust Adaptive Discrete-Time Control Barrier Certificate](https://mlsanity.com/paper/2508.08153/) (2025)

## Abstract (arXiv)

Differentiable predictive control (DPC), a self-supervised learning approach for approximating explicit model predictive control (MPC) policies, offers significant computational advantages over online optimization-based MPC. However, feasibility guarantees, a core requirement for safe control, are currently provided either probabilistically or via online safety filters. The lack of rigorous feasibility guarantees for offline policy optimization remains an open problem. This paper establishes deterministic feasibility guarantees for DPC using a novel topological analysis of the induced reachable safe set, without requiring online safety filters. By exploiting the inherent model-based nature of DPC, in which differentiable system dynamics are embedded directly into the computational graph, we analyze the properties of the learned control policies and the corresponding system states from topological and geometric perspectives. Inspired by our theoretical analysis, we propose a novel self-supervised offline policy learning strategy that utilizes a proxy loss with Control Barrier Functions (CBFs). Crucially, these properties not only significantly improve policy training but also enable the derivation of strict, deterministic feasibility guarantees from a finite number of training samples. Extensive closed-loop simulations validate our theoretical findings, demonstrating that the empirical constraint violations monotonically decrease to zero as the training sample size increases. Ultimately, this work illustrates that DPC policy optimization yields formal safety certificates that are structurally unattainable with conventional black-box methods, e.g., reinforcement learning (RL) or supervised learning-based approximate MPC, thereby providing a new perspective on feasibility guarantees in learning-based control.