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**The maximum principle in optimal control problems with concentrated and distributed delays in controls.**
*(English)*
Zbl 0836.49011

Summary: In the present work there have been posed and studied a general nonlinear optimal problem and a quasilinear optimal problem with fixed time and free right end which contain absolutely continuous monotone delays in phase coordinates and absolutely continuous monotone and distributed delays in controls. For these problems the necessary and, respectively, sufficient conditions of optimality in the form of the maximum principle have been proved.

### MSC:

49K25 | Optimal control problems with equations with ret.arguments (nec.) (MSC2000) |

### Keywords:

necessary conditions; delays in controls; sufficient conditions of optimality; maximum principle
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\textit{G. Kharatishvili} and \textit{T. Tadumadze}, Georgian Math. J. 2, No. 6, 577--591 (1995; Zbl 0836.49011)

### References:

[1] | G. L. Kharatishvili, Z. A. Machaidze, N. I. Markozashvili, and T. A. Tadumadze, Abstract variational theory and its applications to optimal problems with delays. (Russian)Metsniereba, Tbilisi, 1973. |

[2] | R. V. Gamkrelidze and G. L. Kharatishvili, Extremal problems in linear topological spaces I.Math. Systems Theory 1 (1969), No. 3, 229–256. · Zbl 0167.11502 |

[3] | R. V. Gamkrelidze and G. L. Kharatishvili, Extremal problems in linear topological spaces. (Russian)Izv. Akad. Nauk SSSR, Ser. Math. 33 (1969), 781–839. |

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