mlsanityData to 14 Oct 2026

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

arXiv 2606.20197 ↗First posted 18 Jun 2026cs.ROcited by 0

On the map: Deep reinforcement learning methods → RL theory and sample complexity

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.

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.

Builds on

14 of 22 references.

References · 14

  1. 2019Stabilizing Transformers for Reinforcement Learningcited by 270
  2. 2019Understanding and Improving Layer Normalizationcited by 217
  3. 2020Transformers for Modeling Physical Systemscited by 106
  4. 2025Vision-Language-Action Models for Robotics: A Review Towards Real-World Applicationscited by 84
  5. 2021Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overviewcited by 45
  6. 2024The Asymptotic Behavior of Attention in Transformerscited by 16
  7. 2022A Neural ODE Interpretation of Transformer Layerscited by 14
  8. 2025Primal-Dual iLQR for GPU-Accelerated Learning and Control in Legged Robotscited by 8
  9. 2024Model Predictive Control and Reinforcement Learning: A Unified Framework Based on Dynamic Programmingcited by 7
  10. 2025Differentiable Model Predictive Control on the GPUcited by 7
  11. 2023Nonlinear MPC design for incrementally ISS systems with application to GRU networkscited by 6
  12. 2023Input State Stability of Gated Graph Neural Networkscited by 1
2 more
  1. 2025Safe model-based Reinforcement Learning via Model Predictive Control and Control Barrier Functionscited by 1
  2. 2026Transformer Is Inherently a Causal Learnercited by 1

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  1. 2026CA-AC-MPC: CUDA-Accelerated Actor-Critic Model Predictive Control
  2. 2024AC4MPC: Actor-Critic Reinforcement Learning for Nonlinear Model Predictive Control
  3. 2026Guided Riemannian Optimization (GuRO): Bridging Model Predictive Control and Decision Transformers
  4. 2026Stability-Aware Imitation Learning from Model Predictive Control for Autonomous Vehicle Lateral Control: Exact Q-Loss and a Novel Training Procedure
  5. 2024Actor-Critic Physics-informed Neural Lyapunov Control
  6. 2024Autonomous Wheel Loader Navigation Using Goal-Conditioned Actor-Critic MPC
  7. 2026LC-SAC: Lyapunov-Constrained Soft Actor-Critic via Koopman Operator Theory for Trajectory Tracking and Stabilization
  8. 2025Imitation Learning of MPC with Neural Networks: Error Guarantees and Sparsification