Theoretical Fundamentals for Unimodality Estimation of an Objective Functional in the Optimal Control Problem

• Published in: 2019 6th International Conference on Control, Decision and Information Technologies (CoDIT) pp. 767 - 772
• Main Authors: Diveev, Askhat I., Shmalko, Elizaveta Yu, Sofronova, Elena A.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-04-2019
• Subjects: Aerospace electronics; Differential equations; Linear programming; Optimal control; Optimization; Search methods; Trajectory
• ISSN: 2576-3555
• DOI: 10.1109/CoDIT.2019.8820515

The use of various optimization methods and the efficiency of their work strongly depends on the type of functional under investigation. It turned out that in the case of solving optimization problems with a nonlinear compound functional, it is not at all easy to estimate its convexity. And the absence of the unimodality property of the objective function means the instability and low efficiency of the application of gradient extremum search methods. This paper is devoted to the study of the properties of unimodality and convexity of functionals. The nontriviality of the problem of estimating the unimodality of a functional is shown, the concept of a fundamental sequence of functions that are the arguments of the objective functional is introduced, theorems on sufficient conditions for the absence of unimodality of the objective function are formulated and proved.