Passivity-Based Formation Control for Fractional-Order Multiagent Systems With and Without Communication Delay

Because fractional-order differential equations can more accurately model the dynamics of agents, it is very meaningful to investigate the formation control for fractional-order multi-agent systems (FOMASs). Recently, passivity has been widely utilized to tackle various cooperative control problems for integer-order MASs since passive systems are internally stable. Apparently, it is also advantageous to deal with the formation control problem of FOMASs based on the passivity. In this paper, two types of formation control problems for second-order nonlinear FOMASs are discussed by employing the passivity, that is, the cases without and with communication delay, respectively. On the basis of the devised state feedback and adaptive state feedback controllers, several passivity conditions for single fractional-order agent are derived. Furthermore, by selecting suitable distributed state feedback control strategy and exploiting the passivity of fractional-order agent, two formation criteria for the FOMAS are given. In addition, the above obtained results are further extended to the case where communication delay exists in the control input. Finally, two numerical examples are provided to substantiate the effectiveness of the derived formation criteria.