Decembefr 1990 LIDS-P-2012 OPTIMAL ASYMPTOTIC IDENTIFICATION UNDER BOUNDED DISTURBANCES

This paper investigates the intrinsic limitation of identification 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 identification algorithm. The solution involves two steps. First, it is shown that under some compactness conditions on the model set, the asymptotic problem is equivalent to an infinite-horizon problem, where the entire infinite data record is available to compute the estimate. Second, the infinite-horizon problem is analyzed to find optimal inputs for minimizing the worst-case error. Using the 11 norm as the error criterion, an interesting dichotomy of the class of all balanced and convex model sets is obtained: either inputs can be chosen to identify the plant with very small asymptotic error, or no finite set of inputs can yield finite error. Applying the general results on specific model sets, it is shown that the class of all stable plants and the class of all finite-dimensional plants belong to the first category of the dichotomy. Explicit characterization of the optimal inputs for these model sets are also obtained. Research supported by an NSERC fellowship from the government of Canada, and by the NSF under Grant ECS-8552419 Research supported by the AR.O under Grant DAAL03-86-K-0171 Research supported by the NSF under Grant ECS-8552419 and by the ARO under Grant DAAL03-86-K-0171

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