AN EFFICIENT COMPUTATIONAL METHOD FOR SOLVING LARGE-SCALE DIFFERENTIAL SENSITIVITY PROBLEMS

Abstract

An efficient computational method has been developed for differential sensitivity analysis involving large systems of differential equations with a large number of parameters. It is based on both the sensitivity equation method and the theory of balanced realizations. The sensitivity equation method is first used to generate the whole set of sensitivity models (one state-variable model per parameter). A sensitivity model, as well as its corresponding balanced realization, is characterized by three matrices of the same dimension as those in the nominal model: the state matrix, the command matrix, and the output matrix. However, such matrices remain unchanged regardless of the parameter under consideration. Consequently, a single calculation suffices to obtain the balanced realization of all the sensitivity models. Such a representation allows one to rank the state variables according to their degree of controllability/observability. A low-dimension balanced realization is then obtained by keeping only the more controllable/observable state variables. The sensitivity problem solution is finally obtained by time integration of the low-dimension sensitivity models instead of the corresponding full-dimension ones.