Finite-time consensus for variable-order fractional non-linear multi-agent systems under actuator faults and external disturbances

The present investigation aims to address the leader-following consensus issue for variable-order fractional multi-agent systems (VOFMASs) under actuator faults and unknown external disturbances. The Caputo definition for the variable-order fractional (VOF) derivative is used to model the non-linear dynamics of the leader and follower agents. Consequently, two lemmas are developed for the Caputo VOF derivative of the Lyapunov function. In the first case, it is assumed that the multi-agent system (MAS) operates without actuator faults and an adaptive controller is proposed. With the aid of the developed lemmas, assurance is provided for the finite-time bounded cooperative tracking of the VOFMAS despite the presence of unknown external disturbances. In the second case, a novel fault-tolerant controller is designed for the finite-time consensus of the MAS under two common kinds of actuator faults: loss of effectiveness fault and bias fault. Finally, the efficacy of the proposed controller is demonstrated through the presentation of results from three simulation examples.