Lyapunov-based Adaptive Transformer (LyAT) for Control of Stochastic Nonlinear Systems

TL;DR

This paper introduces a Lyapunov-based adaptive transformer controller for stochastic nonlinear systems that provides real-time adaptation and stability guarantees, validated through quadrotor experiments.

Contribution

It develops the first Lyapunov-based adaptive transformer control architecture that estimates uncertainties online with stability guarantees.

Findings

Successfully controls a quadrotor in stochastic environments.

Provides real-time adaptation with probabilistic stability.

Outperforms fixed-weight transformer approaches.

Abstract

This paper presents a novel Lyapunov-based Adaptive Transformer (LyAT) controller for stochastic nonlinear systems. While transformers have shown promise in various control applications due to sequential modeling through self-attention mechanisms, they have not been used within adaptive control architectures that provide stability guarantees. Existing transformer-based approaches for control rely on offline training with fixed weights, resulting in open-loop implementations that lack real-time adaptation capabilities and stability assurances. To address these limitations, a continuous LyAT controller is developed that adaptively estimates drift and diffusion uncertainties in stochastic dynamical systems without requiring offline pre-training. A key innovation is the analytically derived adaptation law constructed from a Lyapunov-based stability analysis, which enables real-time weight updates while guaranteeing probabilistic uniform ultimate boundedness of tracking and parameter estimation errors. Experimental validation on a quadrotor demonstrates the performance of the developed controller.