Mathematics and Computers in Simulation 32 (1990) 447 North-Holland

447

FOREWORD

Central to many fields of pure and applied science is the determination of mathematical models consistent with observations and prior knowledge. When this involves estimating the unknown parameters of approximate models from inexact data, the information available on the various sources of error should be taken into account to derive a proper estimator. This most often involves a statistical description of the errors between the system studied and its model, leading to classical approaches such as Least Squares, Maximum Likelihood or Bayesian estimation. This special issue of Mathematics and Computers in Simulation is devoted to an alternative, determin- istic, approach to the characterization of uncertainty, and its consequences for modelling.

In this approach, the only assumption made about errors is that they lie between known upper and lower bounds. These bounds may correspond to hard facts (such as sensor data sheets or knowledge of the maximal absolute error introduced by a given analog-to-digital converter), or may merely indicate the extreme values of the discrepancies between process and model behaviour that are considered acceptable. The purpose of bounded-error estimation is to characterize the set of all values of the model parameters that are consistent with the data and model structure in the sense that the corresponding errors fall between their prior bounds.

Bounded-error estimation was pioneered more than twenty years ago by F.C. Schweppe and H.S. Witsenhausen and has received renewed attention during the last decade. Small groups working more or less independently have published a number of isolated papers in various journals or conference proceedings, so that it was quite difficult to get any overall idea of the state of the art. This special issue is an attempt at filling this gap, which I would like to dedicate to the memory of Fred C. Schweppe.

With its combination of descriptions of algorithms, discussions of methods, theoretical results, test cases and applications, I feel that it gives a better picture of the current state of the art in bounded-error estimation than could have been written by any one author. I hope you will share this view.

Eric WALTER Guest Editor

037%4754/90/$03.50 0 1990 - Elsevier Science Publishers B.V. (North-Holland)