System Identification Under Bounded Noise

In many physical systems, disturbances are not Gaussian, but they are bounded. This project asks how much that boundedness can improve finite-time system identification when adaptive controllers need uncertainty bounds that hold during online operation in changing environments.

Classical analyses often adopt Gaussian noise assumptions for tractability, leading to the familiar \(\tilde{\mathcal{O}}(1/\sqrt{T})\) convergence rate of least squares. We instead study physically grounded bounded disturbances and develop an online set-membership identification algorithm that leverages this structure to achieve an \(\tilde{\mathcal{O}}(1/T)\) convergence rate, meaning estimation error decreases linearly with the number of samples.

We then prove that \(\tilde{\mathcal{O}}(1/T)\) is the minimax-optimal rate under bounded disturbances, while least squares remains fundamentally limited to the slower \(\tilde{\mathcal{O}}(1/\sqrt{T})\) rate. Together, these results give a finite-time foundation for online and adaptive system identification beyond classical least-squares-based approaches.

Selected outcomes. Non-asymptotic analysis of set-membership uncertainty learning (Li et al., 2024); and a matching minimax lower bound (Zeng et al., 2025).

Timeline. 2024 – present.