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

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.

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