Leader–follower sliding mode formation control of fractional-order multi-agent systems: a dynamic event-triggered mechanism

This chapter examines the concept of the leader–follower formation for fractional-order multi-agent systems (FO-MASs) by utilizing dynamic event-triggered sliding mode control (SMC) method. First, a dynamic event-triggered mechanism (DETM) is designed relying on the combined measurement vector, in which an auxiliary variable is introduced to dynamically adjust the threshold for each fractional-order agent system. Unlike most existing event-triggered communication mechanisms, whose threshold parameters are always fixed, the threshold parameters in our designed event-triggered conditions can be dynamically adjusted according to the fractional-order dynamic rule. Numerical results show that the proposed DETM can achieve a better system performance in reducing the sampling frequency and the expected formation performance. Second, the leader–follower formation control problem is transformed into checking the asymptotic stability problem of the closed-loop system. In addition, due to the memorability of fractional calculus operators, a distinctive condition is established to avoid the occurrence of Zeno behavior reported in existing dynamic event-triggered schemes. Finally, a simulation example is presented to illustrate the effectiveness and feasibility of the dynamic event-triggered SMC method proposed in this chapter.