Distributed Consensus Control for a Network of Incommensurate Fractional-Order Systems

This letter presents a distributed solution for consensus control of a network of single-integrator incommensurate fractional-order systems with nonlinear and uncertain dynamics. To consider a broader class of fractional-order systems, compared to existing results, the fractional derivative orders of agents’ dynamics are assumed non-identical, which makes the distributed control design more challenging. To cope with non-identical fractional derivative orders, the Mittag-Leffler function method is adopted to develop a novel distributed control scheme that guarantees consensus under mild assumptions. To deal with agents’ dynamic uncertainties, the proposed approach is integrated with adaptive neural networks to make the distributed tracking errors for all follower agents converge to a small neighborhood of origin. A numerical example is provided to demonstrate the effectiveness of the proposed method.