ABSTRACT
A physical system is modeled mathematically in terms of: (a) linear and/or nonlinear equations that relate the system's independent variables and parameters to the system's state (i.e., dependent) variables, (b) inequality and/or equality constraints that delimit the ranges of the system's parameters, and (c) one or several quantities, customarily referred to as system responses (or objective functions, or indices of performance) that are to be analyzed as the parameters vary over their respective ranges. The objective of local sensitivity analysis is to analyze the behavior of the system responses locally around a chosen point or trajectory in the combined phase space of parameters and state variables. On the other hand, the objective of global sensitivity analysis is to determine all of the system's critical points (bifurcations, turning points, response extrema) in the combined phase space formed by the parameters, state variables, and adjoint variables, and subsequently analyze these critical points by local sensitivity analysis. The concepts underlying local sensitivity analysis will be presented in Chapters IV and V; specifically, Chapter IV presents the mathematical formalism for sensitivity analysis of linear systems, while Chapter V presents the sensitivity analysis formalism for nonlinear systems with operator responses in the presence of feedback.
