Stable Transformer-Actor-Critic Model Predictive Control: A Contraction Analysis Approach
For control systems practitioners, this work provides a theoretically grounded method to guarantee stability in neural network-based MPC, addressing a key bottleneck in deploying learning-based controllers in safety-critical applications.
The paper introduces a Transformer-Actor-Critic MPC architecture with formal robustness guarantees, proving that Transformers can satisfy global incremental Input-to-State Stability and using Riemannian contraction theory to ensure closed-loop stability. The framework is validated on a nonlinear 3D drone model, achieving certifiably robust policy for target-reaching and obstacle-avoidance.
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.