Necessary Optimality Conditions of the First and Second Order in a Single-Step Control Problem Described by a Difference Equation and a Volterra-Type Integro-Differential Equation
A stepwise optimal control problem described by a set of difference and Volterra-type integro-differential equations and a Bolza functional is considered. Previously, similar problems were studied for the case of differential and ordinary difference equations. Assuming that the control domains are o...
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| Veröffentlicht in: | Computational mathematics and mathematical physics 2024, Vol.64 (10), p.2256-2268 |
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| creator | Mansimov, K. B. Kerimova, A. V. |
| description | A stepwise optimal control problem described by a set of difference and Volterra-type integro-differential equations and a Bolza functional is considered. Previously, similar problems were studied for the case of differential and ordinary difference equations. Assuming that the control domains are open, using a modified version of the increment method, the first and second variations of the quality functional are calculated. Using these variations, an analogue of the Euler equation and a number of constructively verifiable necessary optimality conditions of the second order are proved. |
| doi_str_mv | 10.1134/S0965542524701240 |
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| subjects | Computational Mathematics and Numerical Analysis Difference equations Differential equations Euler-Lagrange equation Mathematics Mathematics and Statistics Optimal Control Optimization Volterra integral equations |
| title | Necessary Optimality Conditions of the First and Second Order in a Single-Step Control Problem Described by a Difference Equation and a Volterra-Type Integro-Differential Equation |
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