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**Optimization of neutral functional-differential inclusions.**
*(English)*
Zbl 1317.49033

Summary: A Bolza problem of optimal control theory with a varying time interval given by convex, nonconvex functional-differential inclusions \((P_N)\), \((P_V)\) is considered. Our main goal is to derive sufficient optimality conditions for neutral functional-differential inclusions, which contain time delays in both state and velocity variables. Both state and endpoint constraints are involved. The presence of constraint conditions implies jump conditions for the conjugate variable, which are typical for such problems. Sufficient conditions under the \(t_1\)-transversality condition are proved incorporating the Euler-Lagrange- and Hamiltonian-type inclusions. Supplementary problems with discrete and discrete approximation inclusions \((P_D)\), \((P_{DA})\) are considered and necessary, and sufficient conditions are given. The basic concept for obtaining optimality conditions are locally adjoint mappings and especially proved equivalence theorems. Furthermore, the application of these results is demonstrated by solving some illustrative examples.

### MSC:

49K21 | Optimality conditions for problems involving relations other than differential equations |

34K09 | Functional-differential inclusions |

34A60 | Ordinary differential inclusions |

54C60 | Set-valued maps in general topology |

### Keywords:

neutral functional-differential inclusions; Bolza problem; optimality conditions; locally adjoint multifunction; transversality
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\textit{E. Mahmudov} and \textit{D. Mastaliyeva}, J. Dyn. Control Syst. 21, No. 1, 25--46 (2015; Zbl 1317.49033)

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