Optimal control problems with delays of general form and with phase constraints

Necessary conditions for an extremum are obtained in the form of a maximum principle in the problem of optimal control of a system described by a differential equation with delays. It is assumed that phase constraints are present in the problem, and the delays in the controls are incommensurable in general. The indicated result is obtained using an abstract theory developed in the paper that is applicable to a large class of optimization problems, including various problems with phase constraints and delays.
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