PUBLISHED PAPERS #05.01
| Yusif Gasimov, Rashad Mastaliyev, Latifa Agamaliyeva, Asif Pashayev. Necessary Optimality Conditions in One Stepwise Nonsmooth Control Problem for Discrete Volterra-Type Systems |
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| Abstract. The paper considers the stepwise optimal control problem described by a difference analog of Volterra type integro-differential equation with a non-differentiable quality criterion. Optimal control problems for the stepwise processes are called optimal control problems for composite systems or multi-stage systems. In the problem under consideration, it is assumed that the right-hand side of the original equation and the quality functional have derivatives in any direction with respect to the state vector. First, using the increment method and some concepts of non-smooth analysis, a necessary optimality condition in terms of generalized directional derivatives is established. Then, based on it, necessary optimality conditions are established, directly expressed by the parameters of the non-smooth problem under consideration. The established result can be used to study the minimax problems for the different stepwise system. |
| Keywords: Volterra type difference equation, stepwise control problem, non-smooth quality functional, directional derivative, optimality, minimax problem |
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| DOI: https://doi.org/10.30546/MaCoSEP2025.1032 |