Topological Feasibility Guarantees for Differentiable Predictive Control

2026-08-10

AI Summary

This work addresses the lack of deterministic feasibility guarantees in offline differentiable predictive control, which hinders its application to safety-critical systems with hard constraints. The authors propose a novel approach that integrates control barrier functions with self-supervised learning to characterize the reachable safe set induced by embedded differentiable dynamics through topological and geometric analysis. Without requiring online safety filters, this method establishes, for the first time, rigorous deterministic feasibility guarantees for differentiable predictive control based on a finite set of training samples. Theoretical analysis reveals a structural advantage enabling the generation of formal safety certificates, while closed-loop simulations demonstrate that empirical constraint violations monotonically converge to zero as the number of training samples increases, thereby validating the effectiveness of the proposed feasibility guarantees.

Abstract

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.

Problem

• differentiable predictive control
• feasibility guarantees
• safe control
• offline policy optimization
• model predictive control

Innovation

• Differentiable Predictive Control
• Topological Feasibility Guarantees
• Control Barrier Functions
• Offline Policy Learning
• Reachable Safe Set