Controllability of nonlinear higher order fractional dynamical systems

Balachandran, K.; Govindaraj, V.; Rodríguez-Germá, Luis; Trujillo, Juan J.

doi:10.1007/s11071-012-0612-y

Cited by 37 publications

(16 citation statements)

References 13 publications

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“…According to Theorem 2.1 of , the controllability Grammian for this system is

\begin{matrix} W (0, 2) & = \int_{0}^{2} {(2 - s)}^{\frac{16}{9}} {((), E_{\frac{17}{9}, \frac{17}{9}} (- 3 {(2 - s)}^{\frac{17}{9}}))}^{2} e^{2 s} normald s \\ = 3.4035 > 0 . \end{matrix}

Therefore the linear system of is controllable on [0,2]. Further, the nonlinear functions

f ((), t, w (t), \int_{0}^{t} g (t, s, w (s))) = \cos w (t) + \int_{0}^{t} \sin w (s) normald s

and

g (t, s, w (s)) = \sin w (s)

satisfy the conditions ( H 1) and ( H 2) of with constants k 1 =1 and k 2 =1 respectively.…”

Section: T‐controllability Of Finite‐dimensional Systemsmentioning

confidence: 98%

Trajectory Controllability of Fractional Integro‐Differential Systems in Hilbert Spaces

Govindaraj¹,

George

2017

Asian Journal of Control

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In this paper, sufficient conditions for trajectory controllability of nonlinear fractional integro‐differential systems involving Caputo fractional derivative of order α∈(1,2] in finite and as well as in infinite dimensional Hilbert spaces are obtained. Our tools of study include set‐valued functions, theory of monotone operators and α‐order cosine family of operators. The main results are well illustrated with the aid of examples.

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“…According to Theorem 2.1 of , the controllability Grammian for this system is

\begin{matrix} W (0, 2) & = \int_{0}^{2} {(2 - s)}^{\frac{16}{9}} {((), E_{\frac{17}{9}, \frac{17}{9}} (- 3 {(2 - s)}^{\frac{17}{9}}))}^{2} e^{2 s} normald s \\ = 3.4035 > 0 . \end{matrix}

Therefore the linear system of is controllable on [0,2]. Further, the nonlinear functions

f ((), t, w (t), \int_{0}^{t} g (t, s, w (s))) = \cos w (t) + \int_{0}^{t} \sin w (s) normald s

and

g (t, s, w (s)) = \sin w (s)

satisfy the conditions ( H 1) and ( H 2) of with constants k 1 =1 and k 2 =1 respectively.…”

Section: T‐controllability Of Finite‐dimensional Systemsmentioning

confidence: 98%

Trajectory Controllability of Fractional Integro‐Differential Systems in Hilbert Spaces

Govindaraj¹,

George

2017

Asian Journal of Control

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“…There are two basic concepts of controllability namely, exact and approximate controllability which are equivalent in finite-dimensional systems and different in the case of infinite-dimensional systems. Klamka [16] discussed the controllability of linear systems in finitedimensional spaces and controllability of fractional evolution dynamical systems in a finite-dimensional space are well established in [4,31]. The concept of approximate controllability of the several types of nonlinear systems under different conditions is discussed in [5,19] and reference therein.…”

Section: Introductionmentioning

confidence: 99%

Approximate controllability of multi-term time-fractional stochastic differential inclusions with nonlocal conditions

Kumar¹,

Pandey²

2019

Malaya J. Mat.

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“…On the other hand, control system is an interconnection of components forming a system configuration that will provide a desired system response. Recently Balachandran et al [25][26][27] established the controllability results for fractional oscillator type dynamical systems by using fixed point theorems and iterative technique.…”

Section: Introductionmentioning

confidence: 99%