Skip to main content
Erschienen in:

09.06.2024

Event-Triggered State Observer Design for a Class of Nonlinear Time-Delay Fractional-Order Systems

verfasst von: Dinh Cong Huong

Erschienen in: Circuits, Systems, and Signal Processing | Ausgabe 9/2024

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This paper studies the problem of designing event-triggered state observers for a class of nonlinear time-delay fractional-order systems. The time delay in the system is assumed to be unknown and non-differentiable but bounded within a closed interval. A novel discrete-time event-triggered fractional-order observer is first designed to provide an estimation vector for the state vector of the considered systems. It is ensured that the estimation vector robustly estimates the state vector of the nonlinear time-delay fractional-order systems. Then, a delay-dependent sufficient condition in terms of a convex optimization problem for the existence of the observer is established based on some lemmas relating to the Caputo derivative estimation of quadratic functions. Finally, three numerical examples demonstrate the validity of the proposed approach.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

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!

ATZelektronik

Die Fachzeitschrift ATZelektronik bietet für Entwickler und Entscheider in der Automobil- und Zulieferindustrie qualitativ hochwertige und fundierte Informationen aus dem gesamten Spektrum der Pkw- und Nutzfahrzeug-Elektronik. 

Lassen Sie sich jetzt unverbindlich 2 kostenlose Ausgabe zusenden.

ATZelectronics worldwide

ATZlectronics worldwide is up-to-speed on new trends and developments in automotive electronics on a scientific level with a high depth of information. 

Order your 30-days-trial for free and without any commitment.

Weitere Produktempfehlungen anzeigen
Literatur
  1. G. Anaya, G.N. Antonio, R.M. Vega, E.G.H. Martinez, Lyapunov functions for a class of nonlinear systems using Caputo derivative. Commun. Nonlinear Sci. Numer. Simul. 43, 91–99 (2017)MathSciNetView Article
  2. E.A. Boroujeni, H.R. Momeni, Non-fragile nonlinear fractional order observer design for a class of nonlinear fractional order systems. Signal Process. 92, 2365–2370 (2012)View Article
  3. S. Boyd, A. Ghaoui, E. Feron, et al. Linear Matrix Inequalities in Systems and Control Theory, in Studies in Applied Mathematics (vol. 15, SIAM, Philadelphia, 1994)
  4. L. Chen, R. Wu, Y. He, L. Yin, Robust stability and stabilization of fractional-order linear systems with polytopic uncertainties. Appl. Math. Comput. 257, 274–284 (2015)MathSciNetView Article
  5. B. Chen, J. Chen, Razumikhin-type stability theorems for functional fractional-order differential systems and applications. Appl. Math. Comput. 254, 63–69 (2015)MathSciNetView Article
  6. A. Coronel-Escamilla, J.F. Gomez-Aguilar, G.V. GuerreroRamirez, On the trajectory tracking control for an SCARA robot manipulator in a fractional model driven by induction motors with PSO tuning. Multibody Sys. Dyn. 43, 257–277 (2018)MathSciNetView Article
  7. D.C. Huong, H. Trinh, Method for computing state transformations of time-delay systems. IET Control Theory Appl. 9, 2405–2413 (2015)MathSciNetView Article
  8. D.C. Huong, M.V. Thuan, Design of unknown input reduced-order observers for a class of nonlinear fractional-order time-delay systems. Int. J. Adapt. Control Signal Process. 32, 412–423 (2018)MathSciNetView Article
  9. T. Kaczorek, Reduced-order fractional descriptor observers for fractional descriptor continuous-time linear system. Bull. Pol. Acad. Sci. Tech. Sci. 62, 889–895 (2014)
  10. T. Kaczorek, Reduced-order perfect nonlinear observers of fractional descriptor discrete-time nonlinear systems. Int. J. Appl. Math. Comput. Sci. 27, 245–251 (2017)MathSciNetView Article
  11. A. Kilbas, H. Srivastava, J. Trujillo, Theory and Application of Fractional Differential Equations (Elsevier, New York, 2006)
  12. Y.H. Lan, L.L. Wang, L. Ding, Y. Zhou, Full-order and reduced-order observer design for a class of fractional-order nonlinear systems. Asian J. Control 18, 1467–1477 (2016)MathSciNetView Article
  13. J.A.T. Machado, A new fractional operator of variable order: application in the description of anomalous diffusion. Physica A Stat. Mech. Appl. 481, 276–283 (2017)MathSciNetView Article
  14. P. Mani, R. Rajan, S. Lakshmanan, Y.H. Joo, Adaptive control for fractional order induced chaotic fuzzy cellular neural networks and its application to image encryption. Inform. Sci. 491, 74–89 (2019)MathSciNetView Article
  15. S. Marzougui, S. Bedoui, A. Atitallah, K. Abderrahim, Parameter and state estimation of nonlinear fractional-order model using Luenberger observer. Circuits Syst. Signal Process. 41, 5366–5391 (2022)View Article
  16. T. N’doye, T.M. Laleg-Kirati, M. Darouach, H. Voos, \(H_{\infty }\) Adaptive observer for nonlinear fractional-order systems. Int. J. Adapt. Control Signal Process. 31, 314–331 (2017)MathSciNetView Article
  17. I. Petras, Fractional-Order Nonlinear Systems (Springer, Berlin, 2011)View Article
  18. M. Pourgholi, E.A. Boroujeni, An iterative LMI-based reduced-order observer design for fractional-order chaos synchronization. Circuits Syst. Signal Process. 35, 1855–1870 (2016)MathSciNetView Article
  19. C. Rajivganthi, F.A. Rihan, S. Lakshmanan, P. Muthukumar, Finite-time stability analysis for fractional-order Cohen–Grossberg BAM neural networks with time delays. Neural Comput. Appl. 29, 1309–1320 (2018)View Article
  20. X. Shao, M. Lyu, J. Zhang, Nonfragile estimator design for fractional-order neural networks under event-triggered mechanism. Disc. Dyn. Nat. Soc. Article ID 6695353 (2021)
  21. H. Trinh, D.C. Huong, S. Nahavandi, Observer design for positive fractional-order interconnected time-delay systems. Trans. Inst. Meas. Control. 41, 378–3911 (2019)View Article
  22. H.T. Tuan, H. Trinh, Stability of fractional-order nonlinear systems by Lyapunov direct method. IET Control Theory Appl. 12, 2417–2422 (2018)MathSciNetView Article
  23. G. Vainikko, Which functions are fractionally differentiable. J. Anal. Appl. 35, 465–487 (2016)MathSciNet
  24. Q. Wang, J. Zhang, D. Ding, D. Qi, Adaptive Mittag–Leffler stabilization of a class of fractional order uncertain nonlinear systems. Asian J. Control 18, 2343–2351 (2016)MathSciNetView Article
  25. A.L. Wu, Z.G. Zeng, Boundedness, Mittag–Leffler stability and asymptotical \(\omega \)-periodicity of fractional-order fuzzy neural networks. Neural net. 74, 73–84 (2016)View Article
  26. A.L. Wu, Z.G. Zeng, X.G. Song, Global Mittag–Leffler stabilization of fractional-order bidirectional associative memory neural networks. Neural net. 177, 489–496 (2016)
  27. B. Xu, B. Li, Event-triggered state estimation for fractional-order neural networks. Mathematics 10, 325 (2022)View Article
  28. X.J. Yang, Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems. Thermal Sci. 21, 1161–1171 (2017)View Article
  29. X.J. Yang, H.M. Srivastava, J.A.T. Machado, New fractional derivative without singular kernel: application to the modelling of the steady heat flow. Thermal Sci. 20, 753–756 (2016)View Article
Metadaten
Titel
Event-Triggered State Observer Design for a Class of Nonlinear Time-Delay Fractional-Order Systems
verfasst von
Dinh Cong Huong
Publikationsdatum
09.06.2024
Verlag
Springer US
Erschienen in
Circuits, Systems, and Signal Processing / Ausgabe 9/2024
Print ISSN: 0278-081X
Elektronische ISSN: 1531-5878
DOI
https://doi.org/10.1007/s00034-024-02745-8