Novel decentralized adaptive strategy for quasi-consensus for fractional heterogeneous multi-agent systems with measurement noise and external disturbances

Abstract Adaptive control has been widely and successfully employed to realize complete consensus in integer-order homogeneous multi-agent systems. Nevertheless, its extension to fractional-order heterogeneous systems poses non-trivial challenges: the weak singularity inherent in fractional calculus impairs the performance of traditional Lyapunov-based adaptive analysis approaches, while the heterogeneous dynamics of individual agents render it necessary to introduce additional control terms or compensators to mitigate the resulting discrepancies. To address these challenges, this paper develops two new lemmas that facilitate the design of Lyapunov-based fractional-order adaptive controllers, thereby efficiently resolving the quasi-consensus analysis problem in fractional-order heterogeneous multi-agent systems. Moreover, for such systems perturbed by measurement noise and external disturbances, a disturbance observer is constructed to achieve precise estimation of external disturbances to improve the robustness of the system. Relying solely on local information exchange among agents, a novel robust distributed adaptive control protocol and a parameter adaptation law are presented. Sufficient conditions guaranteeing quasi-consensus are established by utilizing the designed controllers and the proposed disturbance observer. Finally, extensive numerical simulations are carried out to validate the efficacy of the proposed control strategy. The results illustrate that the proposed lemma and fractional-order adaptive controller design method not only offer an efficient solution to the quasi-consensus problem in fractional-order heterogeneous multi-agent systems but also exhibit considerable theoretical significance and application prospects for quasi-consensus investigations in other fractional-order heterogeneous systems.