Fisher Information on the Performance of Dynamic Systems

Abstract

Recent attempts to develop sustainability theory propose the use of Fisher information as a sustainability index. The approach has been shown to be suitable for the analysis of ecological models, including dynamic simulations as well as optimal control problems where the objective function involves maximizing or minimizing Fisher information. Nevertheless, Fisher information can also be interpreted as a measure of the degree of variability of a dynamic system. The goal of this work is two-fold. First, we study the scope of using the concept of Fisher information as a sustainability index in dynamic systems different in nature from ecological systems. Then we study the behavior of Fisher information in terms of the variability and performance of the dynamic system rather than using it as a sustainability index. The results of three case studies are presented, including two chemical engineering applications (a continuous crystallization system and a series of three continuous stirred tank reactors) and a dynamic model of immunotherapy (therapeutic optimization). We perform parametric analyses, evaluating the behavior of the value of Fisher information against significant model parameters. In general, although its usefulness as a sustainability index might be difficult to interpret and elucidate in some cases, Fisher information not only can indeed be related to the degree of variability of any dynamic system, but also provides useful insights with potential application in process control.