Fundamentals of control-oriented system identification and their application for identification in H∞

This paper examines the system identification problem from the standpoint of control system design. Noting first that nearly all robust control design methods require explicit worst-case/deterministic bounds on the existing plant uncertainty, it is argued that the class of system identification methods which are inherently compatible with robust control design methods-or control-oriented is a subset of the class of system identification methods which yield an explicit worst-case/deterministic bound on the resulting identification error. An abstract theoretical framework for control-oriented system identification is then developed. This framework is inherently worst-case/deterministic in nature, and makes precise such notions as identification error, algorithm convergence, and algorithm optimality from a worst-case/deterministic standpoint. Finally, the abstract theoretical framework is utilized to formulate and solve two related control-oriented system identification problems for stable, linear, shift-invariant, distributed parameter plants. In each of these problems the assumed apriori information is minimal, consisting only of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, and an upper bound on the noise level. In neither case are any assumptions made concerning the structure of either the plant (i.e., dynamic order, relative order, etc.) or the noise (i.e., zero-mean, etc.). The first of these problems involves identification of a point sample of the plant frequency response from a noisy, finite, output time series obtained in response to an applied sinusoidal input with frequency corresponding to the frequency point of interest.