Controllability of mixed Volterra–Fredholm-type integro-differential inclusions in Banach spaces

Chang, Yong-Kui; Chalishajar, Dimplekumar

doi:10.1016/j.jfranklin.2008.02.002

Cited by 57 publications

(32 citation statements)

References 12 publications

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“…We establish now the main result of this section, which has a close relation with the conditions H2 and A2 in [1,2], respectively. Then G is completely continuous.…”

Section: On the Lack Of Exact Controllability In Abstract Control Sysmentioning

confidence: 52%

“…In this paper we show that the examples in [1,2] cannot be recovered as special cases of the abstract results. If the semigroup is compact, then the assumptions H2 and A2 in [1,2], respectively, are valid if and only if X is finite dimensional.…”

Section: Introductionmentioning

confidence: 92%

“…If the semigroup is compact, then the assumptions H2 and A2 in [1,2], respectively, are valid if and only if X is finite dimensional. As a result, the applications are restricted to ordinary differential control systems, see also Triggiani [7] for complementary details.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, the applications are restricted to ordinary differential control systems, see also Triggiani [7] for complementary details. We remark here that there is long list of papers on exact controllability of abstract control system (including, first order systems, second order systems, abstract evolution systems and integro-differential systems) which contain a similar technical error, see for instance [1,2,[8][9][10] and the references therein. Motivated by these papers we extend the results in Triggiani [7] and Henrı´quez [4] for a class of abstract control system which will allow us to discuss the above in detail.…”

Section: Introductionmentioning

confidence: 99%

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Controllability of Volterra–Fredholm type systems in Banach spaces

Hernández

O’Regan

2009

Journal of the Franklin Institute

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“…We establish now the main result of this section, which has a close relation with the conditions H2 and A2 in [1,2], respectively. Then G is completely continuous.…”

Section: On the Lack Of Exact Controllability In Abstract Control Sysmentioning

confidence: 52%

Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Controllability of Volterra–Fredholm type systems in Banach spaces

Hernández

O’Regan

2009

Journal of the Franklin Institute

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“…Controllability of the deterministic and stochastic dynamical control systems in infinite-dimensional spaces is well developed using different kinds of approaches, and the details can be found in various papers (see [1][2][3][4][5] and the references therein). Several authors [6][7][8] studied the concept of exact controllability for systems represented by nonlinear evolution equations, in which the authors effectively used the fixed point approach. Most of the controllability results in infinite-dimensional control system concern the so-called semilinear system that consists of a linear part and a nonlinear part.…”

Section: Introductionmentioning

confidence: 99%

On the approximate controllability of semilinear fractional differential systems

Sakthivel

Ren

Mahmudov

2011

Computers & Mathematics with Applications

186

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a b s t r a c tFractional differential equations have wide applications in science and engineering. In this paper, we consider a class of control systems governed by the semilinear fractional differential equations in Hilbert spaces. By using the semigroup theory, the fractional power theory and fixed point strategy, a new set of sufficient conditions are formulated which guarantees the approximate controllability of semilinear fractional differential systems. The results are established under the assumption that the associated linear system is approximately controllable. Further, we extend the result to study the approximate controllability of fractional systems with nonlocal conditions. An example is provided to illustrate the application of the obtained theory.

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A note on the existence and optimal control for mixed Volterra–Fredholm‐type integrodifferential dispersion system of third order

Patel¹,

Vijayakumar

Nieto

et al. 2022

Asian Journal of Control

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The optimal control problem consists of a performance index subject to a set of differential equations that describes the path of the control and state variables. The main aim of this article is to prove the existence and uniqueness of a mild solution, optimal control, and time‐optimal control of a mixed Volterra–Fredholm‐type third‐order dispersion system. By applying the strongly continuous semigroup theory and the Banach fixed‐point theorem, we prove the existence and uniqueness of the considered system. The optimal control results are proved by using Mazur's lemma, Gronwall's inequality, and the minimizing sequence technique. The discussion on the time‐optimal control of the third‐order dispersion system is also presented.

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Controllability of mixed Volterra–Fredholm-type integro-differential inclusions in Banach spaces

Cited by 57 publications

References 12 publications

Controllability of Volterra–Fredholm type systems in Banach spaces

Controllability of Volterra–Fredholm type systems in Banach spaces

On the approximate controllability of semilinear fractional differential systems

A note on the existence and optimal control for mixed Volterra–Fredholm‐type integrodifferential dispersion system of third order

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