Control oriented system identification: a worst-case/deterministic approach in H∞

The authors 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 a priori 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. 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. This problem leads naturally to the second problem, which involves identification of the plant transfer function in H_∞ from a finite number of noisy point samples of the plant frequency response. Concrete plans for identification algorithms are provided for each of these two problems