IT2 fuzzy adaptive containment control for fractional-order heterogeneous multi-agent systems with input saturation

Abstract

In this paper, the containment control problem of second-order nonlinear heterogeneous multi-agent system is studied. In order to deal with complex uncertainties such as unknown parts, uncertainties, and input constraints in the system, we designed a distributed fuzzy adaptive controller. The interval type-II (IT2) fuzzy set is adopted to deal with the uncertainty of membership functions. We construct a matrix equality and a matrix inequality to deal with the asymmetric Laplace matrix. The controller designed is simple and the designed controller only uses the information of itself and its neighbors. Therefore, it is very easy to be compensated in practice. Finally, a simulation example is introduced to verify the effectiveness of the proposed methods.