Sample Complexity for Worst-Case System Identification Problems

In this paper we treat a general worst-case system identification problem. This problem is worst-case with respect to both noise and system modelling un-certainty. We consider this problem under various a priori information structures. We determine bounds on the minimum duration identification experiment that must be run in order to identify the plant to within a specified guaranteed worst-case error bound. Our results are algorithm independent. We show that this minimum duration is prohibitively long. Based on our results we conclude that worst-case (with respect to noise) system identification requires unrealistic amounts of experimental data.