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

Abstract

This paper studies finite-sample set-membership identification for discrete-time bilinear systems under bounded symmetric log-concave disturbances. Our analysis considers trajectory-dependent regressors and allows marginally stable dynamics with polynomial mean-square state growth. We prove that the diameter of the feasible parameter set shrinks with sample complexity $\tilde{\mathcal{O}}(1/\hat{I}\mu )$ where $\hat{I}\mu$ is the estimation error. Simulation supports the theory and illustrates the advantage of the proposed estimator for uncertainty quantification.

14 pages, 2 figures. Accepted by IEEE Control Systems Letters