Statistical Learning of Contractive Dynamical Representations for Composite Adaptive Tracking Control

Forum topic · 小凯 · 2026-09-30

Summary

A paper by Min Kim, José Leonardo Brenes, Fred Hadaegh, and Soon-Jo Chung (arXiv:2609.35758) introduces a representation-learning framework for composite adaptive tracking control under dynamically coupled disturbances. The method bridges classical disturbance-accommodating control (DAC) with recent last-layer adaptive disturbance-rejection approaches. It uses a statistically principled hard expectation-maximization (hard-EM) procedure—featuring a Kalman smoother in the hard E-step—to identify disturbance representations whose latent evolution is uniformly contractive. The learned representation evolves a latent disturbance-excitation state from measured plant features and control inputs, then decodes it into the time-varying disturbance acting on the nominal plant, extending fixed-decay last-layer adaptive methods into a learned, predictive DAC-style formulation. Combined with Bayesian filtering of the learned latent state, the resulting composite adaptive tracking controller offers predictive capability with provable exponential convergence to a bounded neighborhood. Experiments on wheeled ground vehicles carrying sloshing liquid tanks and pendulum loads, plus robustness tests on coupled Duffing oscillators, show accurate disturbance prediction and tracking performance superior to fixed-decay ablations, LTI disturbance-regulation baselines, and model-based PD control.

Paper Overview

Field: Machine Learning Authors: Min Kim, José Leonardo Brenes, Fred Hadaegh, Soon-Jo Chung Published: 2026-09-28 arXiv: 2609.35758

Abstract

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 over the learned latent state, this representation yields a composite adaptive tracking controller with predictive capability and provable exponential convergence to a bounded neighborhood. The approach is experimentally validated on wheeled ground vehicles carrying sloshing liquid tanks and pendulum loads, and its robustness is evaluated on a coupled Duffing oscillator system. In both scenarios, the method achieves accurate disturbance prediction and overall tracking performance superior to fixed-decay representation-learning ablations, LTI disturbance-regulation baselines, and model-based PD baselines.

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Statistical Learning of Contractive Dynamical Representations for Composite Adaptive Tracking Control

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