Distributed Coordination of Networked Fractional-Order Systems

This paper studies the distributed coordination of networked fractional-order systems over a directed interaction graph. A general fractional-order coordination model is introduced by summarizing three different cases: 1) fractional-order agent dynamics with integer-order coordination algorithms; 2) fractional-order agent dynamics with fractional-order coordination algorithms; and 3) integer-order agent dynamics with fractional-order coordination algorithms. We show sufficient conditions on the interaction graph and the fractional order such that coordination can be achieved using the general model. The coordination equilibrium is also explicitly given. In addition, we characterize the relationship between the number of agents and the fractional order to ensure coordination. Furthermore, we compare the convergence speed of coordination for fractional-order systems with that for integer-order systems. It is shown that the convergence speed of the fractional-order coordination algorithms can be improved by varying the fractional orders with time. Finally, simulation results are presented as a proof of concept.