Considerations Related to Ill-Posed and Well-Posed Problems in System Identification.

TLDR: In this paper, the authors introduce a class of input/output representations (which are called lambda-representations) for linear, time-invariant systems and investigate the effect of input and output uncertainties in the identification experiment, and the treatment of the case when only discrete data are available.

Abstract: : The authors introduce a class of input/output representations (which are called lambda-representations) for linear, time-invariant systems. For many cases of practical interest the identification of one of these representations is mathematically well-posed. Its determination is thus relatively insensitive to certain experimental uncertainties and rational error-in-identification bounds may be found. Impulse response identification almost always leads to an ill-posed problem, so lambda-representation is often an attractive alternate nonparametric model for physical systems which must be identified from input/output records. Among the practical considerations investigated in this report are the effect of input and output uncertainties (noise) in the identification experiment, and the treatment of the case when only discrete data are available. (Modified author abstract)