OPTIMAL ASYMPTOTIC IDENTIFICATIONUNDER BOUNDED DISTURBANCESDavid

This paper investigates the intrinsic limitation of worst-case identiication of LTI systems using data corrupted by bounded disturbances, when the unknown plant is known to belong to a given model set. This is done by analyzing the optimal worst-case asymptotic error achievable by performing experiments using any bounded inputs and estimating the plant using any identiication algorithm. First, it is shown that under some topological conditions on the model set, there is an identiication algorithm which is asymptotically optimal for any input. Characterization of the optimal asymptotic error as a function of the inputs is also obtained. These results hold for any error metric and disturbance norm. Second, these general results are applied to three speciic identiication problems: identiication of stable systems in thè 1 norm, identiication of stable rational systems in the H 1 norm, and identiication of unstable rational systems in the gap metric. For each of these problems, the general characterization of optimal asymptotic error is used to nd near-optimal inputs to minimize the error.

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