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

Hongyu Yi, Chenbei Lu, Jing Yu

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.