Achieving $\widetilde{O}(1/ε)$ Sample Complexity for Bilinear Systems Identification under Bounded Noises
This addresses the challenge of identifying bilinear systems with trajectory-dependent regressors and marginally stable dynamics, offering improved uncertainty quantification for control and system identification applications, though it is incremental relative to prior linear system results.
The paper tackled the problem of finite-sample set-membership identification for discrete-time bilinear systems under bounded symmetric log-concave disturbances, proving that the diameter of the feasible parameter set shrinks with sample complexity $\widetilde{O}(1/ε)$.
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.