Controllability of fractional dynamical systems: A functional analytic approach

Govindaraj, V.; George, Raju K.

doi:10.3934/mcrf.2017020

Cited by 30 publications

(12 citation statements)

References 22 publications

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“…For more results, the interested researchers can refer to previous works. [16][17][18][19][20][21][22][23][24][25] In terms of real-life applications for fractional-order delay optimal control problems, there are several articles available in the literature. In a recent study, Faris et al used proportional fractional-order differential equations with a time delay to examine the profiles of an epidemic model of virulent diseases caused by people who timely report and those who don't register in hospitals for any reason.…”

Section: Introductionmentioning

confidence: 99%

Operator theoretic approach in fractional‐order delay optimal control problems

Vellappandi¹,

Govindaraj²

2022

Math Methods in App Sciences

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This paper investigates the fractional optimal control problem with a single delay in the state by using the operator theoretic approach. In this approach, we first reduce the delay fractional dynamical system into an equivalent operator equation, and then, by providing sufficient conditions to the operators, the existence of an optimal pair is proved for the abstract system. The optimality system for the quadratic cost functional is derived by using the Frechet derivative. Then we relate the operator theoretic approach optimality system to a Hamiltonian system of Pontryagin's minimum principle. The primary goal of this article is to demonstrate the existence of an optimal pair for the fractional‐order delay dynamical system by using a functional minimization theorem in functional analysis. Likewise, the optimality systems for the fractional‐order delay dynamical system are derived by using the functional (either Gateaux or Frechet) derivatives. Finally, we provide two numerical examples that support our theoretical findings.

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Section: Introductionmentioning

confidence: 99%

Operator theoretic approach in fractional‐order delay optimal control problems

Vellappandi¹,

Govindaraj²

2022

Math Methods in App Sciences

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“…Sikora and Klamka [28] studied the constrained controllability of fractional linear systems with delays in control. Govindaraj and George [14] studied the controllability of fractional dynamical systems of functional analytic approach.…”

Section: Introductionmentioning

confidence: 99%

Controllability of nonlinear fractional Langevin delay systems

Kumar

Balachandran

Annapoorani

2019

NAMC

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In this paper, we discuss the controllability of fractional Langevin delay dynamical systems represented by the fractional delay differential equations of order 0 < α, β 1. Necessary and sufficient conditions for the controllability of linear fractional Langevin delay dynamical system are obtained by using the Grammian matrix. Sufficient conditions for the controllability of the nonlinear delay dynamical systems are established by using the Schauders fixed-point theorem. The problem of controllability of linear and nonlinear fractional Langevin delay dynamical systems with multiple delays and distributed delays in control are studied by using the same technique. Examples are provided to illustrate the theory.

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“…[20], [17] used algebraic methods. [43] used geometric approach, while [11], [32], [16] used functional analytic method.…”

Section: Introductionmentioning

confidence: 99%