Approximate Controllability for a Class of Instantaneous and Non-instantaneous Impulsive Semilinear Systems

Kumar, Surendra; Abdal, Syed Mohammad

doi:10.1007/s10883-021-09540-7

Cited by 9 publications

(4 citation statements)

References 11 publications

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“…Further, we have shown that our results can be easily extended to a deterministic control system involving both types of impulse, in which the nonlinear term contains spatial derivatives. (ii) The developed results in this paper involve instantaneous and noninstantaneous impulses simultaneously; thus, we generalize the existing works of Guo and Xu [21], Kumar and Abdal [16], Mokkedem and Fu [19], and Shen and Sun [22]. In fact, using our theory, one can generalize almost all problems related to controllability where instant and noninstant impulses are investigated independently [23][24][25].…”

Section: Introductionmentioning

confidence: 51%

“…The developed results in this paper involve instantaneous and noninstantaneous impulses simultaneously; thus, we generalize the existing works of Guo and Xu [21], Kumar and Abdal [16], Mokkedem and Fu [19], and Shen and Sun [22]. In fact, using our theory, one can generalize almost all problems related to controllability where instant and noninstant impulses are investigated independently [23–25].…”

Section: Introductionmentioning

confidence: 52%

“…Zhang and Liu [15] addressed the existence result for fractional DEs incorporating both the impulses via variational approach. Recently, Kumar and Abdal [16] discussed approximate controllability for a deterministic semilinear DEs involving both types of impulse.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Approximate controllability of stochastic delay differential systems driven by Poisson jumps with instantaneous and noninstantaneous impulses

Kumar

Yadav

2023

Asian Journal of Control

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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.

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Section: Introductionmentioning

confidence: 51%

Section: Introductionmentioning

confidence: 52%

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Approximate controllability of stochastic delay differential systems driven by Poisson jumps with instantaneous and noninstantaneous impulses

Kumar

Yadav

2023

Asian Journal of Control

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“…In our future work, we will consider the following three issues. Firstly, we will discuss the approximate controllability of instantaneous and noninstantaneous impulsive systems [38] driven by fBm with Hurst index H ∈ (0, 1/2). Secondly, we will explore the optimal control for non-instantaneous ISEEs excited by fBm with Hurst parameter H ∈ (0, 1/2).…”

Section: Discussionmentioning

confidence: 99%

Approximate Controllability of Non-Instantaneous Impulsive Stochastic Evolution Systems Driven by Fractional Brownian Motion with Hurst Parameter H∈(0,12)

Liu

Wei

2022

Fractal Fract

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This paper initiates a study on the existence and approximate controllability for a type of non-instantaneous impulsive stochastic evolution equation (ISEE) excited by fractional Brownian motion (fBm) with Hurst index 0<H<1122. First, to overcome the irregular or singular properties of fBm with Hurst parameter 0<H<1122, we define a new type of control function. Then, by virtue of the stochastic analysis theory, inequality technique, the semigroup approach, Krasnoselskii’s fixed-point theorem and Schaefer’s fixed-point theorem, we derive two new sets of sufficient conditions for the existence and approximate controllability of the concerned system. In the end, a concrete example is worked out to demonstrate the applicability of our obtained results.

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Existence, Stability and Optimality of a Semilinear Control System Involving Instantaneous and Non-instantaneous Impulses

Abdal

2024

J Dyn Control Syst

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Approximate Controllability for a Class of Instantaneous and Non-instantaneous Impulsive Semilinear Systems

Cited by 9 publications

References 11 publications

Approximate controllability of stochastic delay differential systems driven by Poisson jumps with instantaneous and noninstantaneous impulses

Approximate controllability of stochastic delay differential systems driven by Poisson jumps with instantaneous and noninstantaneous impulses

Approximate Controllability of Non-Instantaneous Impulsive Stochastic Evolution Systems Driven by Fractional Brownian Motion with Hurst Parameter H∈(0,12)

Existence, Stability and Optimality of a Semilinear Control System Involving Instantaneous and Non-instantaneous Impulses

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