Beyond Asymptotics: Targeted exploration with finite-sample guarantees
This addresses the challenge of ensuring reliable system identification with finite-sample guarantees, which is incremental as it builds on existing non-asymptotic bounds.
The paper tackles the problem of targeted exploration for uncertain linear time-invariant systems with sub-Gaussian disturbances, providing a priori guarantees that optimized exploration inputs achieve desired model parameter accuracy in finite time.
In this paper, we introduce a targeted exploration strategy for the non-asymptotic, finite-time case. The proposed strategy is applicable to uncertain linear time-invariant systems subject to sub-Gaussian disturbances. As the main result, the proposed approach provides a priori guarantees, ensuring that the optimized exploration inputs achieve a desired accuracy of the model parameters. The technical derivation of the strategy (i) leverages existing non-asymptotic identification bounds with self-normalized martingales, (ii) utilizes spectral lines to predict the effect of sinusoidal excitation, and (iii) effectively accounts for spectral transient error and parametric uncertainty. A numerical example illustrates how the finite exploration time influence the required exploration energy.