Statistical Learning of Contractive Dynamical Representations for Composite Adaptive Control

2026-09-28

AI Summary

This study addresses the challenge of composite adaptive tracking control under dynamic coupled disturbances. To this end, it proposes a predictive control framework grounded in representation learning. Specifically, the framework employs statistical methods to identify disturbance dynamics representations exhibiting contraction properties. By introducing a hard expectation-maximization algorithm augmented with a Kalman smoother, it extends conventional fixed-decay approaches into learnable predictive models and integrates Bayesian filtering for precise state estimation. Experimental evaluations on vehicles traversing slippery terrains and coupled Duffing oscillators demonstrate that the proposed method achieves accurate disturbance prediction, significantly enhancing both adaptive tracking performance and control robustness.

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 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.

Problem

• composite adaptive control
• disturbance rejection
• representation learning
• contractive dynamical systems
• tracking control

Innovation

• Representation Learning
• Hard Expectation-Maximization
• Composite Adaptive Control
• Contractive Dynamics
• Disturbance Accommodating Control