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

2026-06-18

AI Summary

This work addresses the challenge of ensuring closed-loop stability in Transformer-based Actor-Critic model predictive control (MPC) by proposing a novel Transformer-Actor-Critic MPC architecture. For the first time, incremental input-to-state stability (δISS) is integrated with Riemannian contraction theory to rigorously analyze the coupled dynamics of neural networks and physical systems, establishing that Transformers satisfy global δISS. The derived theoretical bounds are then incorporated as regularization terms during training to learn control policies with verifiable robustness. Evaluated on nonlinear 3D drone target-reaching and obstacle-avoidance tasks involving complex nonconvex constraints, the proposed method effectively solves these challenging control problems while demonstrating guaranteed closed-loop stability and robustness.

Abstract

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 ($δ$ISS). 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.

Problem

• Stability
• Model Predictive Control
• Transformer
• Actor-Critic
• Closed-loop

Innovation

• Transformer
• Model Predictive Control
• Contraction Theory
• Input-to-State Stability
• Actor-Critic