Fuzzy Adaptive Containment Control for Fractional-Order Heterogeneous Multi-agent Systems with Distributed Time-Varying Delays and Input Saturation

This paper studies the input-constrained containment control problem for a class of fractional-order unknown nonlinear heterogeneous multi-agent systems with distributed time-varying delays under a directed communication network topology. To deal with the unknown time-delay function, we extend the signal permutation method to multiple leaders case and represent it as a bounded function with a generalized consensus tracking error function. To handle input saturation and system uncertainties, we design a distributed adaptive controller using interval type-2 fuzzy logic system theory and projection algorithm, which effectively avoids the complexity caused by general model reduction and ensures the boundedness of estimated parameters. To analyze the convergence of the error system, we construct a new Lyapunov-Krasovskii functional that fully considers the effects of system uncertainties and time delay without requiring the Lyapunov matrix to satisfy a special diagonal form. Then, combining with fractional calculus theory and linear matrix inequality (LMI) method, the sufficient conditions for implementing containment control have been proposed. A new controller design method has also been proposed, ensuring that all followers converge within the convex hull spanned by the leaders. The designed controller is fully distributed and easy to implement in practical applications, as each controller only uses its own and neighboring nodes’ information. Finally, simulation example is presented to demonstrate the effectiveness of the proposed methods.