Optimal Non-Parametric System Identification From Arbitrary Corrupt Finite Time Series: A Control-Oriented Approach

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 apriori 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 aposteriori 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 maps the available apriori and aposteriori information into an "uncertain model" of the plant. The resulting uncertain plant model is comprised of a nominal plant model, a bounded additive output noise, and a bounded additive model uncertainty. The upper bound on the model uncertainty is explicit, worst-case/deterministic in nature, and expressed in terms of both the l
₁
and H
_∞
system norms. Under the assumption that the available apriori information is "correct" for the underlying physical plant, the resulting uncertain plant model has the property that it not only "explains" the available aposteriori information, but will also explain all aposteniori information observed in the future. Because this property hinges on the correctness of the available apriori information, a method is also presented for developing confidence that the available apriori information is in fact correct.