Violation of Object Functional Unimodality and Evolutionary Algorithms for Optimal Control Problem Solution

Abstract

Some common properties of violation of object function unimodality in optimal control problems are considered. Phase constraints and control object models for special symmetric systems are considered. It is shown that for a control problem of a group of objects, given in the form of a symmetric system of equations, for certain initial and terminal conditions the functional is not unimodal. It is claimed that for optimal control problems with non-unimodal functionals it is efficient to use evolutionary algorithms. An example of an optimal control problem for a group of symmetric objects with phase constraints resolved by evolutionary and gradient algorithms is provided.