Conditions of not unimodality of functional in problem of optimal control with phase restrictions
The paper is devoted a research of properties of an unimodality of a functional in a problem of optimal control. In the paper it is proved that under certain conditions the phase restrictions included in a functional in the form of a penalty function make a functional not unimodal. The lack of an unimodality of a functional indicates small effectiveness of use in these problems of gradient methods. It is offered to use evolutionary algorithms for numerical problem solving of optimum control with phase restrictions. The proof of the theorem is provided, that when performing determinate conditions evolutionary algorithms have convergence higher than a random search. Results of a computing experiment in which algorithms of the solution of a problem of optimal control of two mobile robots were compared to phase restrictions are given. Results of an experiment showed effectiveness of application of evolutionary algorithms for numerical problem solving of optimum control with phase restrictions in comparison with gradient methods and a random search.