Skip to main content
Top

2017 | OriginalPaper | Chapter

Relative Controllability of Nonlinear Fractional Delay Dynamical Systems with Time Varying Delay in Control

Author : Joice Nirmala Rajagopal

Published in: Theory and Applications of Non-integer Order Systems

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This paper investigate the relative controllability of nonlinear fractional delay dynamical system with time varying delay in control. The necessary and sufficient conditions for the relative controllability criteria for linear fractional delay system are obtained. The sufficient conditions for the relative controllability of nonlinear fractional delay system are obtained by using Schauder fixed point arguments. Illustrative examples are given to examine the results obtained.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Bellman, R., Cooke, K.L.: Differential Difference Equations. Academic, New York (1963)MATH Bellman, R., Cooke, K.L.: Differential Difference Equations. Academic, New York (1963)MATH
2.
go back to reference Smith, H.: An Introduction to Delay Differential Equations with Application to the Life Sciences. Springer, New York (2011)CrossRefMATH Smith, H.: An Introduction to Delay Differential Equations with Application to the Life Sciences. Springer, New York (2011)CrossRefMATH
3.
go back to reference Halanay, A.: Differential Equations: Stability, Oscillations Time Lags. Academic, New York (1966)MATH Halanay, A.: Differential Equations: Stability, Oscillations Time Lags. Academic, New York (1966)MATH
5.
go back to reference Babiarz, A., Klamka, J., Niezabitowski, M.: Schauder’s fixed point theorem in approximate controllability problems. Int. J. Appl. Math. Comput. Sci. 26(2), 263–275 (2016)CrossRef Babiarz, A., Klamka, J., Niezabitowski, M.: Schauder’s fixed point theorem in approximate controllability problems. Int. J. Appl. Math. Comput. Sci. 26(2), 263–275 (2016)CrossRef
6.
go back to reference Klamka, J., Babiarz, A., Niezabitowski, M.: Banach fixed point theorem in semilinear controllability problems - a survey. Bull. Pol. Ac. Tech. 64(1), 21–35 (2016) Klamka, J., Babiarz, A., Niezabitowski, M.: Banach fixed point theorem in semilinear controllability problems - a survey. Bull. Pol. Ac. Tech. 64(1), 21–35 (2016)
7.
go back to reference Chow, T.S.: Fractional dynamics of interfaces between soft-nanoparticles and rough substrates. Phys. Lett. A 342(1), 148–155 (2005)CrossRef Chow, T.S.: Fractional dynamics of interfaces between soft-nanoparticles and rough substrates. Phys. Lett. A 342(1), 148–155 (2005)CrossRef
8.
go back to reference Magin, R.L.: Fractional Calculus in Bioengineering. Begell House, Redding (2006) Magin, R.L.: Fractional Calculus in Bioengineering. Begell House, Redding (2006)
9.
go back to reference Mainardi, F.: Fractional calculus: some basic problems in continuum and statistical mechanics. In: Carpinteri, A., Mainardi, F. (eds.) Fractals and Fractional calculus in Continuum Mechanics, vol. 378, pp. 291–348. Springer, New York (1997)CrossRef Mainardi, F.: Fractional calculus: some basic problems in continuum and statistical mechanics. In: Carpinteri, A., Mainardi, F. (eds.) Fractals and Fractional calculus in Continuum Mechanics, vol. 378, pp. 291–348. Springer, New York (1997)CrossRef
10.
go back to reference Sabatier, J., Agrawal, O.P., Tenreiro-Machado, J.A.: Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, New York (2007)CrossRefMATH Sabatier, J., Agrawal, O.P., Tenreiro-Machado, J.A.: Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, New York (2007)CrossRefMATH
11.
go back to reference Machado, J.T., Costa, A.C., Quelhas, M.D.: Fractional dynamics in DNA. Commun. Nonlinear. Sci. Numer. Simul. 16(8), 2963–2969 (2011)CrossRefMATH Machado, J.T., Costa, A.C., Quelhas, M.D.: Fractional dynamics in DNA. Commun. Nonlinear. Sci. Numer. Simul. 16(8), 2963–2969 (2011)CrossRefMATH
12.
go back to reference Machado, J.T.: Analysis and design of fractional order digital control systems. Syst. Anal. Model. Simul. 27(2–3), 107–122 (1997)MATH Machado, J.T.: Analysis and design of fractional order digital control systems. Syst. Anal. Model. Simul. 27(2–3), 107–122 (1997)MATH
14.
go back to reference Balachandran, K., Dauer, J.P.: Controllability of perturbed nonlinear delay systems. IEEE Trans. Autom. Control 32, 172–174 (1987)MathSciNetCrossRefMATH Balachandran, K., Dauer, J.P.: Controllability of perturbed nonlinear delay systems. IEEE Trans. Autom. Control 32, 172–174 (1987)MathSciNetCrossRefMATH
15.
go back to reference Balachandran, K., Kokila, J., Trujillo, J.J.: Relative controllability of fractional dynamical systems with multiple delays in control. Comput. Math. Appl. 64(10), 3037–3045 (2012)MathSciNetCrossRefMATH Balachandran, K., Kokila, J., Trujillo, J.J.: Relative controllability of fractional dynamical systems with multiple delays in control. Comput. Math. Appl. 64(10), 3037–3045 (2012)MathSciNetCrossRefMATH
16.
go back to reference Balachandran, K., Zhou, Y., Kokila, J.: Relative controllability of fractional dynamical systems with delays in control. Commun. Nonlinear Sci. Numer. Simul. 17(9), 3508–3520 (2012)MathSciNetCrossRefMATH Balachandran, K., Zhou, Y., Kokila, J.: Relative controllability of fractional dynamical systems with delays in control. Commun. Nonlinear Sci. Numer. Simul. 17(9), 3508–3520 (2012)MathSciNetCrossRefMATH
17.
go back to reference Balachandran, K., Zhou, Y., Kokila, J.: Relative controllability of fractional dynamical systems with distributive delays in control. Comput. Math. Appl. 64(10), 3201–3209 (2012)MathSciNetCrossRefMATH Balachandran, K., Zhou, Y., Kokila, J.: Relative controllability of fractional dynamical systems with distributive delays in control. Comput. Math. Appl. 64(10), 3201–3209 (2012)MathSciNetCrossRefMATH
18.
20.
go back to reference Manzanilla, R., Marmol, L.G., Vanegas, C.J.: On the controllability of differential equation with delayed and advanced arguments. Abstr. Appl. Anal. (2010) Manzanilla, R., Marmol, L.G., Vanegas, C.J.: On the controllability of differential equation with delayed and advanced arguments. Abstr. Appl. Anal. (2010)
21.
go back to reference Mur, T., Henriquez, H.R.: Relative controllability of linear systems of fractional order with delay. Math. Control Relat. Fields 5(4), 845–858 (2015)MathSciNetCrossRefMATH Mur, T., Henriquez, H.R.: Relative controllability of linear systems of fractional order with delay. Math. Control Relat. Fields 5(4), 845–858 (2015)MathSciNetCrossRefMATH
22.
go back to reference Joice Nirmala, R., Balachandran, K.: Controllability of nonlinear fractional delay integrodifferential systems. J. Appl. Nonlinear Dyn. 5, 59–73 (2016)CrossRefMATH Joice Nirmala, R., Balachandran, K.: Controllability of nonlinear fractional delay integrodifferential systems. J. Appl. Nonlinear Dyn. 5, 59–73 (2016)CrossRefMATH
23.
go back to reference Joice Nirmala, R., Balachandran, K., Germa, L.R., Trujillo, J.J.: Controllability of nonlinear fractional delay dynamical systems. Rep. Math. Phys. 77(1), 87–104 (2016)MathSciNetCrossRef Joice Nirmala, R., Balachandran, K., Germa, L.R., Trujillo, J.J.: Controllability of nonlinear fractional delay dynamical systems. Rep. Math. Phys. 77(1), 87–104 (2016)MathSciNetCrossRef
24.
go back to reference Kilbas, A., Srivastava, H.M., Trujillo, J.J.: Theory and Application of Fractional Differential Equations. Elsevier, Amstrdam (2006)MATH Kilbas, A., Srivastava, H.M., Trujillo, J.J.: Theory and Application of Fractional Differential Equations. Elsevier, Amstrdam (2006)MATH
25.
go back to reference Podlubny, I.: Fractional Differential Equations. Academic, New York (1999)MATH Podlubny, I.: Fractional Differential Equations. Academic, New York (1999)MATH
27.
go back to reference Balachandran, K.: Global relative controllability of non-linear systems with time-varying multiple delays in control. Int. J. Control. 46(1), 193–200 (1987)CrossRefMATH Balachandran, K.: Global relative controllability of non-linear systems with time-varying multiple delays in control. Int. J. Control. 46(1), 193–200 (1987)CrossRefMATH
Metadata
Title
Relative Controllability of Nonlinear Fractional Delay Dynamical Systems with Time Varying Delay in Control
Author
Joice Nirmala Rajagopal
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-45474-0_33