# Stable Transformer-Actor-Critic Model Predictive Control: A Contraction Analysis Approach

arXiv: https://arxiv.org/abs/2606.20197 · HTML: https://mlsanity.com/paper/2606.20197/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 14 of its 22 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 14 of 14)

- [Stabilizing Transformers for Reinforcement Learning](https://mlsanity.com/paper/1910.06764/) (2019)
- [Understanding and Improving Layer Normalization](https://mlsanity.com/paper/1911.07013/) (2019)
- [Transformers for Modeling Physical Systems](https://mlsanity.com/paper/2010.03957/) (2020)
- [Vision-Language-Action Models for Robotics: A Review Towards Real-World Applications](https://mlsanity.com/paper/2510.07077/) (2025)
- [Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview](https://mlsanity.com/paper/2110.00675/) (2021)
- [The Asymptotic Behavior of Attention in Transformers](https://mlsanity.com/paper/2412.02682/) (2024)
- [A Neural ODE Interpretation of Transformer Layers](https://mlsanity.com/paper/2212.06011/) (2022)
- [Primal-Dual iLQR for GPU-Accelerated Learning and Control in Legged Robots](https://mlsanity.com/paper/2506.07823/) (2025)
- [Model Predictive Control and Reinforcement Learning: A Unified Framework Based on Dynamic Programming](https://mlsanity.com/paper/2406.00592/) (2024)
- [Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2510.06179/) (2025)
- [Nonlinear MPC design for incrementally ISS systems with application to GRU networks](https://mlsanity.com/paper/2309.16428/) (2023)
- [Input State Stability of Gated Graph Neural Networks](https://mlsanity.com/paper/2305.19235/) (2023)
- [Safe model-based Reinforcement Learning via Model Predictive Control and Control Barrier Functions](https://mlsanity.com/paper/2512.04856/) (2025)
- [Transformer Is Inherently a Causal Learner](https://mlsanity.com/paper/2601.05647/) (2026)

## Abstract (arXiv)

Actor-Critic Model Predictive Control (MPC) effectively addresses complex, non-convex control problems, but guaranteeing the closed-loop stability of sequence-based learning models within these pipelines remains challenging. This paper introduces a novel Transformer-Actor-Critic MPC architecture with formal robustness guarantees. First, we prove that Transformer networks can satisfy global incremental Input-to-State Stability (δISS). We then leverage Riemannian contraction theory to analyze the interconnected dynamics between the physical plant and the predictive neural network. Finally, we integrate these theoretical bounds as a training regularizer to yield a certifiably robust policy. The framework is validated on a nonlinear 3D drone model executing target-reaching and obstacle-avoidance maneuvers.