New data processing technique based on the optimal control theory

Abstract

The problem of choosing the best set of parameters for a given mathematical model that adequately describes independent experimental data is formulated in terms of the optimal control theory. The sum of squares of discrepancies between experimental data and their analogues calculated within the framework of a given mathematical model of a process is minimized. A solution to the problem is found, and conditions for optimally choosing the parameters of the mathematical model are established. The search algorithm is generalized for the case where a penalty function is present, and an efficient way of including inequality constraints is suggested. The algorithm was tested by finding the thermal conductivity of single crystals (Ioffe-Ioffe classical experiment), thermal diffusivity of a thin plate, and parameters of gene expression during the fruit fly (Drosophila melanogaster) embryo evolution.