Iterative Learning Bipartite Consensus Control for Fractional-Order Switched Nonlinear Heterogeneous MASs with Cooperative and Antagonistic Interactions

The coordination of switched fractional-order nonlinear heterogeneous multi-agent systems (FONHMASs) with cooperative and antagonistic interactions presents significant challenges due to the complex coupling of switched fractional-order dynamics. Crucially, existing control methods typically rely on integer-order assumptions and precise system modeling, which are inadequate for capturing the inherent non-local memory behaviors of fractional dynamics. Furthermore, they generally assume fixed agent dynamics, and cannot be applied to switched FONHMASs where the continuity of agents’ dynamics is violated at switching instants. Considering the constraints of precise modeling difficulties and limited task time for switched FONHMASs in practice, a distributed Dα-type iterative learning control (ILC) protocol is proposed to achieve bipartite consensus in the presence of cooperative and antagonistic interactions. Also, without relying on repetitive initial conditions, based on a presented initial state learning mechanism and Dα-type ILC protocol, the bipartite consensus error convergence property with each iteration is achieved. Additionally, in consideration of external disturbances, the robustness of the iterative bipartite consensus controller for the switched FONHMASs is analyzed. Simulation results confirm that the switched FONHMASs achieve the convergence and robustness of the bipartite consensus errors along the iteration direction. In addition, the proposed Dα-type ILC protocol achieves a maximum root-mean-square-error (MRMSE) of 0.0168 in time domain, significantly outperforming the integer-order ILC (MRMSE = 0.3601) and fractional-order PID control (MRMSE = 0.7550), confirming its superiority.