The general question of sensitivity arises in most systems where mathematical models are used for the purpose of analysis and system design. In order to be able to give a quantitative formulation of the problem, the mathematical model is usually assumed to be known exactly. This assumption is, strictly speaking, unrealistic since there is always a certain discrepancy between the actual system and its mathematical model. This discrepancy may be caused either by erroneous modeling due to the assumption of ideal behavior of certain system components or due to the erroneous selection of system parameters and or due to the manufacturing tolerances, environmental changes such as temperature and humidity, etc., or when a range of operating conditions is contemplated. In many systems uncertainties are present which prevent the formulation of a deterministic model for the system.
However, once a realistic model is chosen, sensitivity plays an important role in assessing the behavior of the system or its components under varying conditions.
Sensitivity considerations have provided a fundamental motivation for the use of feedback and are largely responsible for its development into what is called modern control theory, employing principles such as optimization, adaptation, etc. Therefore, it is quite natural that the basic concepts in this area were already given in the fundamental literature on feedback control systems. Almost all systems in nature whether physical, biological, chemical, electrical, mechanical, social, economical, have feedback loops and thus one can utilize the concepts of sensitivity. The application of the sensitivity concept is therefore wide and far reaching.
The basic objective of this issue is to bring together recent results on sensitivity from a wide range of system types and applications such as linear, nonlinear, large scale, decision analysis, management information systems, economic and power systems.
As the reader would expect, a complete coverage of the application of sensitivity to various fields would require more than one issue or volume. Hence, because of the time and space limitation we could not cover many other important topics such as transportation systems and societal systems.
As we shall see in scanning this special issue, the powerful tools of sensitivity analysis can be used to analyze systems which only a few years ago were thought to be amenable only to heuristic investigation.
The paper entitled, "System Partial Inverses for Sensitivity, Adaptivity and Estimation" by Aravena and Porter, presents a unified approach to parameter estimation, parameter sensitivity and parameter adaptivity analysis. The main motivation of this paper is derived from the fact that adaptivity and .I.