# MPC-Guided Safe Reinforcement Learning and Lipschitz-Based Filtering for Structured Nonlinear Systems

arXiv: https://arxiv.org/abs/2512.12855 · HTML: https://mlsanity.com/paper/2512.12855/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Safe and constrained RL, one of 15 directions in Deep reinforcement learning methods.
- Builds on 3 of its 15 references that are in the map.
- First posted on arXiv 14 Dec 2025.

## Placed in

- Deep reinforcement learning methods / [Safe and constrained RL](https://mlsanity.com/deeprl/safe-and-constrained-rl/)

## Builds on (most cited first, 3 of 3)

- [Combining system identification with reinforcement learning-based MPC](https://mlsanity.com/paper/2004.03265/) (2020)
- [The Definitive Guide to Policy Gradients in Deep Reinforcement Learning: Theory, Algorithms and Implementations](https://mlsanity.com/paper/2401.13662/) (2024)
- [Attitude Control of Highly Maneuverable Aircraft Using an Improved Q-learning](https://mlsanity.com/paper/2210.12317/) (2022)

## Abstract (arXiv)

Modern engineering systems, such as autonomous vehicles, flexible robotics, and intelligent aerospace platforms, require controllers that are robust to uncertainties, adaptive to environmental changes, and safety-aware under real-time constraints. RL offers powerful data-driven adaptability for systems with nonlinear dynamics that interact with uncertain environments. RL, however, lacks built-in mechanisms for dynamic constraint satisfaction during exploration. MPC offers structured constraint handling and robustness, but its reliance on accurate models and computationally demanding online optimization may pose significant challenges. This paper proposes an integrated MPC-RL framework that combines stability and safety guarantees of MPC with the adaptability of RL. During training, MPC defines safe control bounds that guide the RL component and that enable constraint-aware policy learning. At deployment, the learned policy operates in real time with a lightweight safety filter based on Lipschitz continuity to ensure constraint satisfaction without heavy online optimizations. The approach, which is validated on a nonlinear aeroelastic wing system, demonstrates improved disturbance rejection, reduced actuator effort, and robust performance under turbulence. The architecture generalizes to other domains with structured nonlinearities and bounded disturbances, offering a scalable solution for safe artificial-intelligence-driven control in engineering applications.