# Statistical Learning of Contractive Dynamical Representations for Composite Adaptive Control

arXiv: https://arxiv.org/abs/2609.35758 · HTML: https://mlsanity.com/paper/2609.35758/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 27 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 8 of 8)

- [Learning robust perceptive locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2201.08117/) (2022)
- [Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds](https://mlsanity.com/paper/2205.06908/) (2022)
- [Adapting Rapid Motor Adaptation for Bipedal Robots](https://mlsanity.com/paper/2205.15299/) (2022)
- [Neural Contractive Dynamical Systems](https://mlsanity.com/paper/2401.09352/) (2024)
- [Asynchronous Deep Model Reference Adaptive Control](https://mlsanity.com/paper/2011.02920/) (2020)
- [MAGIC-VFM: Meta-learning Adaptation for Ground Interaction Control with Visual Foundation Models](https://mlsanity.com/paper/2407.12304/) (2024)
- [Enhancing Sample Efficiency and Uncertainty Compensation in Learning-based Model Predictive Control for Aerial Robots](https://mlsanity.com/paper/2308.00570/) (2023)
- [Learning disturbance models for offset-free reference tracking](https://mlsanity.com/paper/2312.11409/) (2023)

## Abstract (arXiv)

We present a representation-learning framework for composite adaptive tracking control under dynamically coupled disturbances. The framework connects classical disturbance-accommodating control (DAC) to recent last-layer adaptive disturbance-rejection methods. Specifically, we introduce a statistically principled hard expectation-maximization (hard-EM) procedure, with a Kalman smoother in the hard E-step, to identify dynamical representations of disturbance whose latent evolution is uniformly contractive. The learned representation evolves a latent disturbance-excitation state from measured plant features and control inputs and decodes that state into the time-varying disturbance acting on the nominal plant, thereby extending prior "fixed-decay" last-layer adaptive methods to a learned, predictive DAC-style formulation. Combined with Bayesian filtering of the learned latent state, this representation yields a composite adaptive tracking controller with predictive capability and provable exponential convergence to a bounded neighborhood. We validate our approach experimentally on a slippery ground vehicle carrying a liquid-sloshing tank and a pendulum load, and we further assess its robustness on a system of coupled Duffing oscillators. Across both settings, the method achieves accurate disturbance prediction and improved overall tracking performance relative to fixed-decay representation-learning ablations, LTI disturbance-accommodating baselines, and model-based PD baselines.