Global leader-following consensus in finite time for fractional-order multi-agent systems with discontinuous inherent dynamics subject to nonlinear growth

• Published in: Communications in nonlinear science & numerical simulation Vol. 37; p. 100888
• Main Authors: Wang, Xiaohong, Wu, Huaiqin, Cao, Jinde
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.08.2020; Elsevier Science Ltd
• Subjects: Continuity (mathematics); Differential equations; Discontinuous inherent dynamics; Filippov differential inclusion; Fractional multi-agent systems; Global consensus in finite time; Lyapunov functional approach; Mathematical functions; Multiagent systems; Nonlinear control; Nonlinear dynamics; Nonlinear systems; Fractional multi-agent systems; Global consensus in finite time; Lyapunov functional approach; Filippov differential inclusion; Discontinuous inherent dynamics
• ISSN: 1751-570X; 1007-5704; 1878-7274
• DOI: 10.1016/j.nahs.2020.100888

This paper considers the global leader-following consensus of fractional-order multi-agent systems (FMASs), where the inherent dynamics is modeled to be discontinuous, and subject to nonlinear growth. Firstly, based on convex functions, three formulas on fractional derivative are established respectively. By applying the proposed formulas, a principle of convergence in finite-time for absolutely continuous functions is developed. Secondly, a new nonlinear control protocol, which includes discontinuous factors, is designed. Under fractional differential inclusion framework, by means of Lyapunov functional approach and Clarke’s non-smooth analysis technique, the sufficient conditions with respect to the global consensus are achieved. In addition, the setting time is explicitly evaluated for the global leader-following consensus in finite time. Finally, two illustrative examples are provided to check the correction of the obtained results in this paper.