scholarly journals Approximate controllability of impulsive system involving state-dependent delay and variable delay in control via fundamental solution

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2293-2313
Author(s):  
Syed Abdal ◽  
Surendra Kumar
Keyword(s):  
Fundamental Solution ◽  
Hilbert Spaces ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Impulsive System ◽  
Variable Delay ◽  
New Class ◽  
State Dependent ◽  
Semilinear Control Systems ◽  
State Dependent Delay

This article is concerned with the approximate controllability for a new class of impulsive semilinear control systems involving state-dependent delay and variable delay in control in Hilbert spaces. We formulate new sufficient conditions which guarantee the existence of solution to the considered system. We use the theory of fundamental solution, Krasnoselskii?s and Schauder?s fixed point theorems to establish our major results. Finally, two examples are constructed which demonstrate the effectiveness of obtained results.

Approximate controllability of impulsive fractional integro-differential equation with state-dependent delay in Hilbert spaces

2018 ◽  
Vol 36 (2) ◽  
pp. 603-622 ◽  
Author(s):  
Yong Zhou ◽  
S Suganya ◽  
M Mallika Arjunan ◽  
B Ahmad
Keyword(s):  
Differential Equation ◽  
Hilbert Spaces ◽  
Approximate Controllability ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Integro Differential Equation ◽  
State Dependent ◽  
State Dependent Delay ◽  
Non Linear ◽  
Approximately Controllable

Abstract In this paper, the problem of approximate controllability for non-linear impulsive fractional integro-differential equation with state-dependent delay in Hilbert spaces is investigated. We study the approximate controllability for non-linear impulsive integro-differential systems under the assumption that the corresponding linear control system is approximately controllable. By utilizing the methods of fractional calculus, semigroup theory, fixed-point theorem coupled with solution operator, sufficient conditions are formulated and proved. Finally, an example is provided to illustrate the proposed theory.

Optimization of exact controllability for fractional impulsive partial stochastic differential systems via analytic sectorial operators

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zuomao Yan ◽  
Yong-Hui Zhou
Keyword(s):  
Hilbert Spaces ◽  
Measure Of Noncompactness ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Exact Controllability ◽  
Differential Systems ◽  
New Class ◽  
Sectorial Operators ◽  
State Dependent ◽  
State Dependent Delay

AbstractIn this paper, we consider the optimization problems of exact controllability for a new class of fractional impulsive partial stochastic differential systems with state-dependent delay in Hilbert spaces. By utilizing suitable fixed point approach without imposing severe compactness condition on the operators, the theory of analytic sectorial operators, stochastic analysis, and the Hausdorff measure of noncompactness, some sufficient conditions are derived for achieving the required results. Finally, an example is provided to illustrate the obtained theory.

Approximate controllability of non-instantaneous impulsive semilinear measure driven control system with infinite delay via fundamental solution

2020 ◽  
Author(s):  
Surendra Kumar ◽  
Syed Mohammad Abdal
Keyword(s):  
Fundamental Solution ◽  
Differential Equations ◽  
Control Systems ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Existence Of A Solution ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
New Class

Abstract This article investigates a new class of non-instantaneous impulsive measure driven control systems with infinite delay. The considered system covers a large class of the hybrid system without any restriction on their Zeno behavior. The concept of measure differential equations is more general as compared to the ordinary impulsive differential equations; consequently, the discussed results are more general than the existing ones. In particular, using the fundamental solution, Krasnoselskii’s fixed-point theorem and the theory of Lebesgue–Stieltjes integral, a new set of sufficient conditions is constructed that ensures the existence of a solution and the approximate controllability of the considered system. Lastly, an example is constructed to demonstrate the effectiveness of obtained results.

scholarly journals Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mourad Kerboua ◽  
Amar Debbouche ◽  
Dumitru Baleanu
Keyword(s):  
Control Systems ◽  
Hilbert Spaces ◽  
Dynamic Systems ◽  
Approximate Controllability ◽  
Dynamic Control ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Stochastic Dynamic ◽  
Deterministic Control ◽  
Stochastic Dynamic Systems

We study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for approximate controllability is formulated and proved. An example is also given to provide the obtained theory.

scholarly journals Approximate controllability of second order impulsive systems with state-dependent delay in banach spaces

2019 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Soniya Singh ◽  
◽  
Sumit Arora ◽  
Manil T. Mohan ◽  
Jaydev Dabas ◽  
...  
Keyword(s):  
Banach Spaces ◽  
Approximate Controllability ◽  
Second Order ◽  
Impulsive Systems ◽  
State Dependent ◽  
State Dependent Delay

scholarly journals Approximate controllability of delayed semilinear control systems

2005 ◽  
Vol 2005 (1) ◽  
pp. 67-76 ◽  
Author(s):  
Lianwen Wang
Keyword(s):  
Differential Equations ◽  
Control Systems ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Semilinear Control Systems

We deal with the approximate controllability of control systems governed by delayed semilinear differential equations y˙(t)=Ay(t)+A1y(t−Δ)+F(t,y(t),yt)+(Bu)(t). Various sufficient conditions for approximate controllability have been obtained; these results usually require some complicated and limited assumptions. Results in this paper provide sufficient conditions for the approximate controllability of a class of delayed semilinear control systems under natural assumptions.

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