Controllability of systems with a general nonlocal condition

Pinaud, Matthieu F.; Henrı́quez, Hernán R.

doi:10.1016/j.jde.2020.03.029

Cited by 14 publications

(8 citation statements)

References 22 publications

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“…The conception of controllability was first initiated and established by Kalman [13] in 1960, and since then it is the matter of prime importance for the researchers worldwide. The results of existence and controllability for various differential systems of integer and fractional order involving Riemann-Liouville and Caputo derivatives have closely been demonstrated in many artefacts (refer [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]and references therein).…”

Section: Introductionmentioning

confidence: 74%

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Non-instantaneous Impulsive Riemann-Liouville Fractional Differential Systems: Existence and Controllability Analysis

Sahijwani¹,

Sukavanam²,

Haq³

2021

Preprint

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The article is dedicated towards the study of fractional order non-linear differential systems with non-instantaneous impulses involving Riemann-Liouville derivatives with fixed lower limit and appropriate integral type initial conditions in Banach spaces. First, mild solution of the system is constructed and subsequently its existence is proven using Banach's fixed point theorem. Then, results of approximate controllability are established using concept of fractional semigroup and an iterative technique. Suitable examples are given in the end supporting the methodology along with pointing out correction in examples presented in previous articles.

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Section: Introductionmentioning

confidence: 74%

“…Also, the present findings can be extended for the partial approximate controllability or finite approximate controllability of the considered system with general nonlocal conditions. For some idea, see [9,20,21,24].…”

Section: Discussionmentioning

confidence: 99%

Non-instantaneous Impulsive Riemann-Liouville Fractional Differential Systems: Existence and Controllability Analysis

Sahijwani¹,

Sukavanam²,

Haq³

2021

Preprint

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“…Controllability is one of the basic concepts of modern control theory and plays an important role in pole assignment and optimal control. Therefore, the controllability of various integer or fractional order systems has been widely studied by many researchers in recent years, see [24,48,16,12,2,10,28,17] and the references therein. Controllability includes exact controllability and approximate controllability in infinite dimensional systems.…”

mentioning

confidence: 99%

Approximate controllability of fractional neutral evolution systems of hyperbolic type

Hou

Zhou

et al. 2022

EECT

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<p style='text-indent:20px;'>In this paper, we deal with fractional neutral evolution systems of hyperbolic type in Banach spaces. We establish the existence and uniqueness of the mild solution and prove the approximate controllability of the systems under different conditions. These results are mainly based on fixed point theorems as well as constructing a Cauchy sequence and a control function. In the end, we give an example to illustrate the validity of the main results.</p>

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“…Controllability theory can also be set in the framework of multivalued dynamics occurring when the nonlinearity f or the nonlocal condition D are given by a multivalued map (see e.g. [3], [29] or [33]). We believe that our solvability method works also in this framework.…”

mentioning

confidence: 99%

“…If conditions (f 1 ) and ( 29) hold then f is a Carathéodory function and for every q ∈ C([0, T ], W ), f (•, q(•)) is measurable (q is the pointwise limit of simple functions, then f (•, q(•)) is the pointwise limit of measurable functions). Moreover, if (29) holds also (f 2 3 ) holds with α(t) = L(t) and…”

mentioning

confidence: 99%

$ L^p $-exact controllability of partial differential equations with nonlocal terms

Malaguti

Perrotta

Taddei

2022

EECT

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<p style='text-indent:20px;'>The paper deals with the exact controllability of partial differential equations by linear controls. The discussion takes place in infinite dimensional state spaces since these equations are considered in their abstract formulation as semilinear equations. The linear parts are densely defined and generate strongly continuous semigroups. The nonlinear terms may also include a nonlocal part. The solutions satisfy nonlocal properties, which are possibly nonlinear. The states belong to Banach spaces with a Schauder basis and the results exploit topological methods. The novelty of this investigation is in the use of an approximation solvability method which involves a sequence of controllability problems in finite-dimensional spaces. The exact controllability of nonlocal solutions can be proved, with controls in <inline-formula><tex-math id="M2">\begin{document}$ L^p $\end{document}</tex-math></inline-formula> spaces, <inline-formula><tex-math id="M3">\begin{document}$ 1<p<\infty $\end{document}</tex-math></inline-formula>. The results apply to the study of the exact controllability for the transport equation in arbitrary Euclidean spaces and for the equation of the nonlinear wave equation.</p>

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Controllability of systems with a general nonlocal condition

Cited by 14 publications

References 22 publications

Non-instantaneous Impulsive Riemann-Liouville Fractional Differential Systems: Existence and Controllability Analysis

Non-instantaneous Impulsive Riemann-Liouville Fractional Differential Systems: Existence and Controllability Analysis

Approximate controllability of fractional neutral evolution systems of hyperbolic type

$ L^p $-exact controllability of partial differential equations with nonlocal terms

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