The intrinsic limitation of worst-case identification of linear time-invariant systems using data corrupted by bounded disturbances, when the unknown plant is known to belong to a given model set, is studied. This is done by analyzing the optimal worst-case asymptotic error achievable by performing experiments using any bounded input and estimating the plant using any identification algorithm. It is shown that under some topological conditions on the model set, there is an identification algorithm which is asymptotically optimal for any input, and the optimal asymptotic error is characterized as a function of the inputs. These results, which hold for any error metric and disturbance norm, are applied to three specific identification problems: identification of stable systems in the l/sub 1/ norm, identification of stable rational systems in the H/sub infinity / norm and identification of unstable rational systems in the gap metric. For each of these problems, the general characterization of optimal asymptotic error is used to find near-optimal inputs to minimize the error.
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机译：当已知未知植物属于给定模型集时，研究了使用有界干扰破坏的数据对线性时不变系统进行最坏情况识别的固有局限性。这是通过分析可通过使用任何有界输入进行实验并使用任何识别算法估算植物而获得的最佳最坏情况渐近误差来完成的。结果表明，在模型集的某些拓扑条件下，存在一种对于任何输入都渐近最优的识别算法，并且最优渐近误差的特征在于输入的函数。这些结果适用于任何误差度量和扰动范数，适用于三个特定的识别问题：l / sub 1 /范数中的稳定系统的识别，H / sub无穷大/范数中的稳定有理系统的识别以及差距度量中的不稳定有理系统。对于这些问题中的每一个，都使用最佳渐近误差的一般特征来找到接近最优的输入，以最大程度地减小误差。
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