Paper Overview
Stochastic Adaptive Control for Systems with Nonlinear Parameterization: Almost Sure Stability and Tracking
Takeaway: The paper develops adaptive estimation and control methods for nonlinear stochastic systems and proves almost-sure stability with long-run tracking guarantees.
Why It Matters
Nonlinear stochastic models appear in recurrent neural networks, social dynamics, signal processing, and other networked systems. When unknown parameters enter nonlinearly, the estimation problem becomes nonconvex and classical adaptive control assumptions can be too strong for closed-loop stability.
Technical Contribution
- Studies nonlinear stochastic systems whose updates combine nonlinear functions, linear dynamics, and additive stochastic noise.
- Develops an online nonlinear weighted least-squares estimator and proves global strong consistency.
- Avoids restrictive persistent-excitation requirements by using conditions suited to stochastic closed-loop trajectories.
- Builds an adaptive controller with attenuating excitation and proves global stability with long-run average tracking.
Who Should Read This
Researchers in adaptive control, stochastic systems, nonlinear identification, learning-based control, network dynamics, robotics, and systems theory.
Links
@misc{zhang2026stochastic,
title = {{Stochastic Adaptive Control for Systems with Nonlinear Parameterization: Almost Sure Stability and Tracking}},
author = {Zhang, L. and Wahlberg, B. and Zhang, S.},
year = {2026},
eprint = {2604.06980},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2604.06980}
}