Approximate boundary controllability of Sobolev-type stochastic differential systems. (English) Zbl 1296.93026
Summary: The objective of this paper is to investigate the approximate boundary controllability of Sobolev-type stochastic differential systems in Hilbert spaces. The control function for this system is suitably constructed by using the infinite dimensional controllability operator. Sufficient conditions for approximate boundary controllability of the proposed problem in Hilbert space is established by using contraction mapping principle and stochastic analysis techniques. The obtained results are extended to stochastic differential systems with Poisson jumps. Finally, an example is provided which illustrates the main results.
MSC:
| 93B05 | Controllability |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 93E03 | Stochastic systems in control theory (general) |
| 34K50 | Stochastic functional-differential equations |
Keywords:
approximate boundary controllability; contraction mapping principle; Hilbert space; semigroup theory; stochastic differential systemsReferences:
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