Optimal controls problems for some impulsive stochastic integro-differential equations with state-dependent delay. (English) Zbl 1499.34384
Summary: In this paper, optimal control problems for a class of stochastic functional integral-differential equations in Hilbert spaces are investigated. First, the existence of mild solutions is investigated using stochastic analysis theory, fixed point theorems, and Grimmer’s resolvent operator theory. Following that, the existence requirements of optimal pairs of systems governed by stochastic partial integro-differential equations with infinite delay are discussed. The results are achieved by the use of a combination of Lipschitz and Carathéodory conditions. At the end of the paper, an illustration is supplied to help highlight the key findings.
MSC:
| 34K30 | Functional-differential equations in abstract spaces |
| 34K45 | Functional-differential equations with impulses |
| 45J05 | Integro-ordinary differential equations |
| 45N05 | Abstract integral equations, integral equations in abstract spaces |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 34K50 | Stochastic functional-differential equations |
| 37L55 | Infinite-dimensional random dynamical systems; stochastic equations |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
Keywords:
integro-differential equations; mild solution; fixed point theorem; phase space; resolvent operator; optimal control; state-dependent delay; impulsive partial stochastic systemReferences:
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