Distributed Coordination Algorithms for Multiple Fractional-Order Systems

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