Group multiple lags consensus of fractional-order nonlinear leader-following multi-agent systems via adaptive control

Yunlong Zhang (1) , Guoguang Wen (1) , Zhaoxia Peng (2) , Yongguang Yu (1) , Ahmed Rahmani (3)

1 School of Science, Beijing Jiaotong University
2 School of Transportation Science and Engineering, Beihang University, Beijing, China
3 MOCIS - Méthodes et Outils pour la Conception Intégrée de Systèmes

In this paper, group multiple lags consensus of fractional-order leader-following multi-agent systems with nonlinear dynamics are investigated, in which two kinds of lag consensus are considered. One is said to be outergroup lag consensus, which means that different group leaders reach lag consensus. The other one is called innergroup lag consensus, that is to say, the followers will reach lag consensus with their own group leader. Based on Mittag-Leffler stability for fractional-order systems, algebraic graph theory, a class of novel control protocols is designed and the corresponding sufficient conditions are derived to guarantee the achievement of group multiple lags consensus. Furthermore, considering parametric uncertainties, an adaptive control technology is employed to solve the group multiple lags consensus for fractional order multi-agent systems, and the corresponding adaptive control protocols and sufficient conditions are proposed. Finally, numerical simulations are given to demonstrate the effectiveness of the obtained results.

Mots clés: Multi-agent systems; lag consensus; adaptive control; fractional-order; Mittag-Leffler stability

Domaines: Informatique [cs]; Mathématiques [math]

Yunlong Zhang, Guoguang Wen, Zhaoxia Peng, Yongguang Yu, Ahmed Rahmani. Group multiple lags consensus of fractional-order nonlinear leader-following multi-agent systems via adaptive control. Transactions of the Institute of Measurement and Control, 2018, 41 (5), pp.1313-1322. ⟨10.1177/0142331218777570⟩. ⟨hal-02117332⟩