Containment control for fractional order MASs with nonlinearity and time delay via pull-based event-triggered mechanism.

• The containment control of fractional order multi-agent systems with nonlinearity is considered. • A control protocol with time delay for fractional order multi-agent systems is designed. • A pull-based event-triggered control law combined time delay is designed. • Mittag-Leffler function based method is adopted instead of Lyapunov method. • Zeno behavior is precluded by the strict proof. The containment control for fractional order multi-agent systems with nonlinearity and time delay is investigated in this article. Firstly, a distributed control protocol with fixed time delay is proposed for the purpose of achieving containment control for nonlinear fractional order multi-agent systems. Secondly, by using the pull-based event-triggered mechanism, a distributed event-based control law with time delay is further given to accomplish containment control for fractional order multi-agent systems with nonlinearity. In this way, the controller of each agent is merely updated at its own trigger moments. Hence, it can decrease network correspondence congestion and lower computational cost. Thanks to the stability theory of fractional order calculus, matrix theory, and properties of Mittag-Leffler function, the feasibility of the designed control protocols is confirmed. Furthermore, the Zeno behavior is precluded by the strict proof. Ultimately, two simulation examples are used to illustrate the availability of above theoretical analysis respectively. [ABSTRACT FROM AUTHOR]