Fuzzy adaptive containment control for fractional-order heterogeneous nonlinear multi-agent systems with mixed time-varying delays

This study investigates the issue of containment control (CC) of multi-agent systems (MASs) that are heterogeneous, nonlinear, and fractional-order while taking practical scenarios into account, such as uncertainties, unknown nonlinearities, time-varying state delays, and distributed time-varying delays. A fully distributed adaptive observer is created for each follower in accordance with the communication topology information among agents. This observer is designed to estimate the convex combination information of the leaders. The approach utilizes interval type-2 fuzzy set theory and adaptive methods to design a distributed containment control strategy that only uses the self-information of the followers and neighbor nodes' information. Sufficient conditions for implementing containment control are given. A new Lyapunov-Krasovskii functional (LKF) is constructed, and the stability of the system with feedback loop is proven using fractional-order theory and inequality methods. Lastly, a simulation example is presented to illustrate the efficacy of the proposed approach.