Approximate controllability of stochastic delay differential systems driven by Poisson jumps with instantaneous and noninstantaneous impulses. (English) Zbl 07892432
Summary: Control systems in which instantaneous and noninstantaneous impulses occur simultaneously are difficult to handle. In this article, we investigate the solvability and approximate controllability for a new category of stochastic differential equations steered by Poisson jumps with instantaneous and noninstantaneous impulses. Utilizing the theory of fundamental solution, stochastic analysis, the measure of noncompactness, and the fixed-point approach, we establish the presence of a mild solution for the proposed system. We have also constructed a new set of sufficient constraints that assures approximate controllability of the considered system. Next, we discuss the existence of a solution and approximate controllability for an impulsive deterministic control system in which the nonlinear term contains spatial derivatives. Lastly, two examples are presented to encapsulate the abstract results.
© 2023 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd.
© 2023 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd.
MSC:
| 93-XX | Systems theory; control |
Keywords:
approximate controllability; fixed-point theory; instantaneous impulses; noninstantaneous impulses; Poisson jumps; stochastic delay differential systemsReferences:
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