Abstract
The objective of this paper is to investigate the approximate controllability of a semilinear impulsive stochastic system with nonlocal conditions and Poisson jumps in a Hilbert space. Nonlocal initial condition is a generalization of the classical initial condition and is motivated by physical phenomena. The results are obtained by using Sadovskii’s fixed point theorem. Finally, an example is provided to illustrate the effectiveness of the obtained result.
Highlights
1 Introduction The concept of controllability plays a major role in both finite and infinite dimensional spaces for systems represented by ordinary differential equations and partial differential equations
In order to fill this gap, this paper considers the approximate controllability of semilinear stochastic control systems with nonlocal conditions using Sadovskii’s fixed point theorem
The goal of the present research work is to focus on studying the approximate controllability of a semilinear impulsive stochastic system with nonlocal conditions and Poisson jumps of the form dz(t) = Az(t) + Bu(t) + f t, z(t) dt + σ t, z(t) dw(t)
Summary
The concept of controllability plays a major role in both finite and infinite dimensional spaces for systems represented by ordinary differential equations and partial differential equations. Dynamics of many evolutionary processes with such a characteristic arise naturally and are often, for example, population dynamics, control theory, physics, biology, medicine, etc. These perturbations can be well-approximated as instantaneous change of state or impulses. Luo and Liu [17] established the existence and uniqueness theory of mild solutions to stochastic partial functional differential equations with Markovian switching and Poisson jumps. The goal of the present research work is to focus on studying the approximate controllability of a semilinear impulsive stochastic system with nonlocal conditions and Poisson jumps of the form dz(t) = Az(t) + Bu(t) + f t, z(t) dt + σ t, z(t) dw(t).
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