Approaches to Numerical Solution of Optimal Control Problem Using Evolutionary Computations

Askhat Diveev,Elena Sofronova,Sergey Konstantinov

doi:10.3390/app11157096

Abstract

Two approaches to the numerical solution of the optimal control problem are studied. The direct approach is based on the reduction of the optimal control problem to a nonlinear programming problem. Another approach is so-called synthesized optimal control, and it includes the solution of the control synthesis problem and stabilization at some point in the state space, followed by the search of stabilization points and movement of the control object along these points. The comparison of these two approaches was carried out as the solution of the optimal control problem as a time function cannot be directly used in the control system, although the obtained discretized control can be embedded. The control object was a group of interacting mobile robots. Dynamic and static constraints were included in the quality criterion. Implemented methods were evolutionary algorithms and a random parameter search of piecewise linear approximation and coordinates of stabilization points, along with a multilayer network operator for control synthesis.

Highlights

The focus of this research was the study of numerical methods for solving the optimal control problem
An indirect approach is based on the Pontryagin maximum principle, which transforms the original optimization problem into a boundary one, which is numerically solved by shooting methods or as a finite-dimensional optimization problem [2]
The contribution of this paper is that we show that the optimal control of a group of robots under phase constraints is not unimodal, and it is necessary to use methods of global optimization, for example, evolutionary algorithms

Summary

Introduction

The focus of this research was the study of numerical methods for solving the optimal control problem. A group of objects should move from given initial states to terminal ones while avoiding obstacles in a minimum time. The problem belongs to the class of infinite-dimensional optimization. There are two approaches to solve it numerically [1]. A direct approach is based on a discretization of the control function and reduction to the finite-dimensional optimization. An indirect approach is based on the Pontryagin maximum principle, which transforms the original optimization problem into a boundary one, which is numerically solved by shooting methods or as a finite-dimensional optimization problem [2]

Methods

Results

Conclusion