Deterministic Sensitivity Theory for Nonlinear Systems: The Forward and the Adjoint Method

摘要

The main aspects underlying the rigorous mathematical formulation of deterministic sensitivity theory for nonlinear systems are presented; this formulation is based on the work by Cacuci and employs concepts and methods of nonlinear functional analysis. The functional analytic concepts underlying sensitivity theory are briefly reviewed in Section II. The rigorous formulation of sensitivity theory for nonlinear systems is presented in Section III. Section III.A presents the sensitivity theory for nonlinear systems with operator-type responses. Section III.B presents the development of the sensitivity theory for nonlinear systems with responses defined at critical points of a function of the system's state vector and parameters (maxima, minima, and saddle points). Section III.C presents sensitivity theory for nonlinear systems with feedback. Finally, Section IV summarizes and highlights the main points underlying deterministic sensitivity theory for nonlinear systems and discusses the potential of using functional analytic concepts to extend further the scope of this theory. 37 refs. (ERA citation 11:033283)