Consensus and Adaptive Consensus for Nonlinear Fractional-Order Multiagent Systems via Passivity

This paper focuses on the consensus and the adaptive consensus problems for a kind of nonlinear fractional-order multi-agent systems (FOMASs) via passivity analysis. A passivity criterion is first derived for the FOMASs via state feedback control, based on which the relationship between output strict passivity and consensus for FOMASs is then revealed leveraging the Laplace transform method and the properties of Mittag-Leffler functions, thereby generalizing the existing passivity-based consensus results for the nonlinear MASs with fractional-order dynamics. Furthermore, an adaptive state feedback strategy is developed for consensus of the FOMASs with inaccurate coupling gains. Different from the traditional integer-order adaptive strategies, the designed fractional-order adaptive law, based on the Caputo fractional-order derivative and the communication topology, is able to effectively regulate the coupling gain, which provides a more realistic representation of system performance metrics due to the memory and hereditary properties of fractional-order derivatives. Simulation results from two numerical examples verify the effectiveness of the presented approaches.