Hard and Tight Upper Bounds on The Model Uncertainty in Linear Estimation of Restricted Complexity Models

This paper considers the problem of uncertainty quentification in linear estimation of restricted complexity models. In the paper, the plant identifier and the uncertainty identifier run in parallel. While the plant identifier provides an optimal estimate in some sense, the bound on the difference between this estimate and the true system is characterized by a sequence of rational functions generated by the uncertainty identifier. The importance of this sequence is that each member of this sequence is truly a hard upper bound of the uncertainty in L2 sense independent of the order of the approximant. Moreover, as the order n of the approximant increases, the bound derived gets tighter and tighter and eventually converges to the actual uncertainty bound as n ¿ ¿. Thus in estimation of restricted complexity models, the possibly conflict goals of providing an optimal estimate as well as a hard upper bound on the model uncertainty is resolved by dividing the traditional identifier into two parts the plant identifier and the uncertainty identifier as proposed in the paper.