A worst case identification method using time series data

Abstract

In this paper we formulate and solve a control-oriented system identification problem for single-input, single-output, linear, shift-invariant, distributed parameter plants. In this problem the available a priori information is minimal, consisting only of worst-case/deterministic, time dependent, upper and lower bounds on the plant impulse response and the additive output noise. The available a posteriori information consists of a corrupt finite output time series obtained in response to a known, non-zero but otherwise arbitrary, applied input. A novel system identification method is presented for this problem. This method yields an “uncertain model” of the plant, which is comprised of a nominal plant model, a bounded additive output noise, and a bounded additive model uncertainty measured in both the l ₁ and H _∞ system norms. Both the identification method and the resulting uncertain model are computationally simple and possess certain desirable properties.