Achieving $\tilde{O}(1\mathrm{/}\epsilon )$ Sample Complexity for Bilinear Systems Identification under Bounded Noises

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 $\tilde{O}(1\mathrm{/}\epsilon )$. Simulation supports the theory and illustrates the advantage of the proposed estimator for uncertainty quantification.