Optimal Control of Transition Processes of Objects on Quick-Speed in a Multi-Criteria Environment

We analyze the known problems of optimal control of speed (OCS) and methods for their solution. It is shown that the use of the one criteria in these tasks (the speed criterion) does not sufficiently reflect real situations. The solution of the OCS problem in real situations leads to a deviation from the nominal or optimal values of a number of other indicators. Proceeding from this, a generalization of the OCS problem is considered taking into account other indicators as a criterion for optimal control. In this aspect, three generalized statements of the OCS problem are analyzed, where in the first formulation, the OCS task is expanded with additional constraints on other indicators; in the second setting, other indicators were used as criteria alongside with the performance criterion; and in the third formulation, the expansion of the formulation is considered with the introduction of restrictions also on the criteria themselves, formed from other measured indicators. In the article, the most general — the third multicriteria problem is considered as the subject of research and the necessary condition for optimality of its solution in the form of the maximum principle is obtained. A traditional and iterative scheme for solving the generalized by OCS problem is presented, based on the obtained necessary optimality condition, in contrast to the traditional criteria, which are also dependent on the degree of preference. 

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