Behaviour of fractional discrete-time consensus models with delays for summator dynamics

• Autorzy: Girejko E. , Mozyrska D. , Wyrwas M.

Identyfikatory

DOI

10.24425/124255

• Języki publikacji: EN

Abstrakty

EN

The leader-following consensus problem of fractional-order multi-agent discrete-time systems with delays is considered. In the systems, interactions between agents are defined like in Krause and Cucker-Smale models, but the memory is included by taking both the fractional-order discrete-time operator on the left hand side of the nonlinear systems and the delays. Since in practical problems only bounded number of delays can be considered, we study the fractional order discrete-time models with a finite number of delays. The models of opinions under consideration are investigated for single- and double-summator dynamics of discrete-time by means of analytical methods as well as computer simulations.

Słowa kluczowe

EN

fractional calculus; consensus; single-summator; double-summator; discrete-time models with delays

PL

rachunek ułamkowy; konsensus; model dyskretny; opóźnienia

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2018
• Tom: Vol. 66, nr 4
• Strony: 403--410
• Opis fizyczny: Bibliogr. 10 poz., wykr.

Twórcy

autor

Girejko E.

• Faculty of Computer Science, Bialystok University of Technology, 45A Wiejska St., 15-351 Białystok, Poland

autor

Mozyrska D.

• Faculty of Computer Science, Bialystok University of Technology, 45A Wiejska St., 15-351 Białystok, Poland

autor

Wyrwas M.

• Faculty of Computer Science, Bialystok University of Technology, 45A Wiejska St., 15-351 Białystok, Poland

Bibliografia

• [1] X. Su, L. Wu, and P. Shi, “Sensor networks with random link failures: distributed filtering for t-s fuzzy systems”, IEEE Trans. Ind. Inf. 9(3), 1739–1750 (2013).
• [2] R. Murray and R. Olfati-Saber, “Consensus problems in networks of agents with switching topology and time-delays”, IEEE Trans. Autom. Control 49(9), 1520–1533 (2004).
• [3] H. Chu, Y. Cai, and W. Zhang, “Consensus tracking for multiagent systems with directed graph via distributed adaptive protocol”, Neurocomputing 166, 8–13 (2015).
• [4] E. Girejko, L. Machado, A.B. Malinowska, and N. Martins, “On consensus in the Cucker-Smale type model on isolated times scales”, Discrete Contin. Dyn. Syst. Ser. S 11(1), 77–89 (2018).
• [5] S. Shen, W. Li, and W. Zhu, “Consensus of fractional-order multiagent systems with double integrator under switching topologies”, Discrete Dynamics in Nature and Society, p. 7, 2017.
• [6] G. Ren, Y. Yu, and S. Zhang, “Leader-following conensus of fractional nonlinear multiagent systems”, Mathematical Problems in Engineering 2015, 8 (2015).
• [7] Y. Cao, Y. Li, W. Ren, and Y.Q. Chen, “Distributed coordination of networked fractional-order systems”, IEEE Transactions on Systems, Man, and Cybernetics – Part B: Cybernetics 40(2), 362–370 (2010).
• [8] M.Wyrwas, D. Mozyrska, and E. Girejko, “Fractional discretetime consensus models for single- and double-summator dynamics”, International Journal of Systems and Science, 2018, DOI: 10.1080/00207721.2018.1442511.
• [9] D. Mozyrska, M. Wyrwas, and P. Ostalczyk, “Stability conditions for fractional-order linear equations with delays”, Bull. Pol. Ac.: Tech. 66(4), 449–454 (2018).
• [10] R.S. Varga, Gerˇsgorin and His Circles, Berlin, Springer-Verlag, 2004.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).