Bipartite Output Synchronization of Fuzzy Fractional Output-Coupled Networks via Membership Function-Dependent Adaptive Control

This article focuses on the bipartite output synchronization for a type of fuzzy fractional output-coupled networks based on fractional-order fuzzy adaptive strategies. Firstly, in view of the unavailability of state information caused by irresistible factors and the coexistence of cooperative and competitive relations in reality, a class of T-S fuzzy fractional networks with output couplings is established under the signed graph framework. Next, a type of membership function-dependent fractional adaptive schemes is presented to automatically regulate the control gains, some criteria of bipartite output synchronization are derived based on the characteristic of the signed topology instead of traditional gauge transformation method. Particularly, a pinning adaptive control scheme is employed to investigate bipartite output synchronization for fuzzy fractional output-coupled networks with the positive-definite output matrix, which determines the pinning nodes just dependent of the cooperative links among nodes in signed graph. The developed criteria are finally confirmed by some examples. Note to Practitioners—Considering the unavailability of state information caused by irresistible factors and the coexistence of cooperative and competitive relations in real networked systems, the bipartite output synchronization issue of fuzzy fractional cooperative-antagonistic networks is concerned in this study, which has potential applications in opinion dynamics of social networks, bidirectional formation of uncrewed aerial vehicles. A type of membership function-dependent fractional adaptive scheme and its pinning form are developed to automatically regulate the control gains, which reflects the influence of fuzzy rules on control and improves the previous fuzzy-independent controller design. In theoretical analysis, based on the decomposition of Laplacian matrix of the signed graph, a direct analysis method is developed instead of traditional gauge transformation, which not only provides a new and more effective tool for the investigation of bipartite synchronization or consensus, but also weakens the requirement on topology connectivity. As a result, the proposed fuzzy-dependent adaptive controller and direct analysis technique have great theoretical values and wide practical engineering applications.