Closed Loop System Identification With Known Feedback: A Non Asymptotic Viewpoint.

In this paper, we develop a method to estimate the parameters of an unknown closed loop discrete time LTI system with feedback. This is accomplished using regularized least squares and a subspace algorithm for system identification. Under several assumptions on the underlying system dynamics we obtain non-asymptotic bounds on estimation error and demonstrate that our algorithm converges to the true parameters of the system over time. We show that even when the dimension of the underlying system is unknown, accurate reduced order approximations can be recovered. We also present extensions of these results to unstable open loop plants and more general multiple input multiple output systems. Simulations demonstrate the efficacy of this method for single input single output systems and its potential for use in adaptive control.