Achieving $\widetilde{O}(1/ε)$ Sample Complexity for Bilinear Systems Identification under Bounded Noises

2026-03-21

AI Summary

This study addresses finite-sample set-membership identification for discrete-time bilinear systems under bounded symmetric log-concave noise, tackling the challenges posed by trajectory-dependent regressors and marginally stable dynamics that permit polynomial growth in the mean-square state norm. Within a set-membership identification framework, the authors combine symmetric log-concave noise modeling with non-asymptotic probabilistic analysis to establish, for the first time, that the diameter of the feasible parameter set contracts at a sample complexity of $\widetilde{O}(1/\varepsilon)$ under mild noise assumptions and complex bilinear dynamics. This result extends beyond the limitations of existing theory for linear systems, and numerical simulations demonstrate the superior performance of the proposed estimator in uncertainty quantification.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

This paper studies finite-sample set-membership identification for discrete-time bilinear systems under bounded symmetric log-concave disturbances. Compared with existing finite-sample results for linear systems and related analyses under stronger noise assumptions, we consider the more challenging bilinear setting with trajectory-dependent regressors and allow marginally stable dynamics with polynomial mean-square state growth. Under these conditions, we prove that the diameter of the feasible parameter set shrinks with sample complexity $\widetilde{O}(1/ε)$. Simulation supports the theory and illustrates the advantage of the proposed estimator for uncertainty quantification.

Problem

• bilinear systems
• sample complexity
• set-membership identification
• bounded noises
• finite-sample

Innovation

• bilinear systems
• set-membership identification
• sample complexity
• bounded noise
• trajectory-dependent regressors