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  4. Algorithm of the successive approximation method for optimal control problems with phase restrictions for mechanics tasks

Algorithm of the successive approximation method for optimal control problems with phase restrictions for mechanics tasks

MMC.
2022;
Volume 9, Number 3
: pp. 734–749
https://doi.org/10.23939/mmc2022.03.734
Received: July 19, 2022
Revised: August 30, 2022
Accepted: September 01, 2022

Mathematical Modeling and Computing, Vol. 9, No. 3, pp. 734–749 (2022)

Authors:
  1. A. Dzyuba
  2. A. Torskyy
1
Oles Honchar Dnipro National University
2
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NASU; Lviv Polytechnic National University

The algorithm of the method of successive approximations for problems of optimal control in the presence of arbitrary restrictions on control and phase variables is proposed.  The approach is based on the procedures of consistent satisfaction of the necessary conditions of optimality in the form of Pontryagin's maximum principle.  The algorithm application for the problems of weight optimization of power elements of structures in the presence of constraints of strength, rigidity, and technological requirements is demonstrated.

successive approximations method
Pontryagin's maximum principle
phase and terminal constraints
optimal design of structures
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